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This is very marginal, but as Theta30 mentioned in a comment, the word "brooch" is pronounced /broʊtʃ/ (or in British English, /brəʊtʃ/), the same as "broach" (in fact, both words have the same etymological origin according to the Oxford English Dictionary).

I would guess that all speakers use /ʊ/ in these two words; if there are any speakers that use /uː/, that would require some more explanation. It is known that at least some dialects had lengthening of Old English /u/ to Middle English /oː/ in open syllables: this is supposed to be the origin of the Early Modern English pronunciations of above < OE abufan and love < OE lufu with long /uː/ that show up from time to time in poetry. (See "http://english.stackexchange.com/questions/73645".) This could at least explain */wu:d/, if that pronunciation exists. I have no idea how */wu:l/ could be explained, if it exists.

Example words taken from Jakub Marian’s useful article on the pronunciation of “oo”, which Josh linked to in a comment on a related question, as well as OneLook Dictionary Seach. OneLook and its indexed dictionaries were used along with the Oxford English Dictionary to find etymological information.

Information on the Great Vowel shift taken in part from this great "Great Vowel Shift" handout from Anthony Kroch's website, which I also learned about from Josh's answer to the following question: Why do "bomb" and "tomb" have different pronunciations?

This is very marginal, but as Theta30 mentioned in a comment, the word "brooch" is pronounced /broʊtʃ/ (or in British English, /brəʊtʃ/), the same as "broach" (in fact, both words have the same etymological origin according to the Oxford English Dictionary).

I would guess that all speakers use /ʊ/ in these two words; if there are any speakers that use /uː/, that would require some more explanation. It is known that at least some dialects had lengthening of Old English /u/ to Middle English /oː/ in open syllables: this is supposed to be the origin of the Early Modern English pronunciations of above < OE abufan and love < OE lufu with long /uː/ that show up from time to time in poetry. (See "https://english.stackexchange.com/questions/73645".) This could at least explain */wu:d/, if that pronunciation exists. I have no idea how */wu:l/ could be explained, if it exists.

Example words taken from Jakub Marian’s useful article on the pronunciation of “oo”, which Josh linked to in a comment on a related question, as well as OneLook Dictionary Seach. OneLook and its indexed dictionaries were used along with the Oxford English Dictionary to find etymological information.

Information on the Great Vowel shift taken in part from this great "Great Vowel Shift" handout from Anthony Kroch's website, which I also learned about from Josh's answer to the following question: Why do "bomb" and "tomb" have different pronunciations?

Here are the main shortening environments.

As fas as I can tell, short "oo" is possible before /k d t f m/, and after /w/. Here is an overview of these shortening environments.

• Both "oo" sounds generally come from the same source, Early Modern English /uː/. The /ʊ/ sound is the result of a shortening process that was only partially predictable and that seems to have been active both before and after another vowel change that un-rounded /ʊ/ to /ʌ/ in most environments.

• Early Modern English /uː/ generally developed via the Great Vowel Shift from Middle English /oː/, which in turn mostly came from Old English /oː/, which is represented in modern scholarly transcriptions as "ō". This o-sound is the origin of the spelling ⟨oo⟩.

• Middle English /uː/ (usually spelled "ou" or "ow") mostly turned into the Early Modern English diphthong /aʊ/ via the Great Vowel Shift. However, before a labial consonant such as /p/ /f/ /v/ /m/, this change was inhibited, and Middle English /uː/ became Early Modern English /uː/, merging with the reflex of /oː/. This led to some un-etymological spellings such as "room" < MidE "roum(e)", "rowm(e)" < OE rūm and "droop" < MidE "droupe", "drowp(e)" Old Norse drúpa.

• Another spelling quirk is that some words that were likely pronounced with /uːv/ or /uv/ in Early Modern English were spelled with "ov", with a single "o": examples are "behove" < OE bi-/behōfian (now commonly spelled "behoove" in the United States) and "love" < OE lufu (which probably usually had /uv/, but dialectally or poetically could have /uːv/), as well as the non-native verbs "move" and "prove" which have somewhat unclear phonetic development to modern /uːv/.

-ook. Early Modern English /uːk/ seems to have quite regularly been shortened to /ʊk/, and consistently after the sound change of /ʊ/ to /ʌ/. (Speaking here of the pronunciations that contributed to modern standard English; it is well known that there is regional variability.) So there are very few exceptions to the ⟨ook⟩-/ʊk/ correspondence in modern English, and they all seem to be words that originated at a time period after shortening was active.

I actually don’t know what vowel people use for these words in areas that generally lack the “short oo” sound. I would guess /ʊ/ or /ʌ/; if there are any speakers that use /uː/, that would require some more explanation. It is known that at least some dialects had lengthening of Old English /u/ to Middle English /oː/ in open syllables: this is supposed to be the origin of the Early Modern English pronunciations of above < OE abufan and love < OE lufu with long /uː/ that show up from time to time in poetry. (See "http://english.stackexchange.com/questions/73645".) This could at least explain */wu:d/, if that pronunciation exists. I have no idea how */wu:l/ could be explained, if it exists.

• Both "oo" sounds generally come from the same source, Early Modern English /uː/. The /ʊ/ sound is the result of a shortening process that was only partially predictable and that seems to have been active both before and after another vowel change that un-rounded /ʊ/ to /ʌ/ in most environments. Some dialects in Northern English lack the /ʊ/ to /ʌ/ change entirely, and therefore lack the sound /ʌ/.

• Early Modern English /uː/ generally developed via the Great Vowel Shift from Middle English /oː/, which in turn mostly came from Old English /oː/, which is represented in modern scholarly transcriptions as "ō". This o-sound is the origin of the spelling ⟨oo⟩.

• Middle English /uː/ (usually spelled "ou" or "ow") mostly turned into the Early Modern English diphthong /aʊ/ via the Great Vowel Shift. However, before a labial consonant such as /p/ /f/ /v/ /m/, this change was inhibited, and Middle English /uː/ became Early Modern English /uː/, merging with the reflex of /oː/. This led to some un-etymological spellings such as "room" < MidE "roum(e)", "rowm(e)" < OE rūm and "droop" < MidE "droupe", "drowp(e)" Old Norse drúpa.

• Another spelling quirk is that some words that were likely pronounced with /uːv/ or /uv/ in Early Modern English were spelled with "ov", with a single "o": examples are "behove" < OE bi-/behōfian (now commonly spelled "behoove" in the United States) and "love" < OE lufu (which probably usually had /uv/, but dialectally or poetically could have /uːv/), as well as the non-native verbs "move" and "prove" which have somewhat unclear phonetic development to modern /uːv/.

-ook. Early Modern English /uːk/ seems to have quite regularly been shortened to /ʊk/, and consistently after the sound change of /ʊ/ to /ʌ/. (Speaking here of the pronunciations that contributed to modern standard English; it is well known that there is regional variability, and some regions apparently don't show shortening in "-ook" words.) So there are very few exceptions to the ⟨ook⟩-/ʊk/ correspondence in modern standard English, and they all seem to be words that originated at a time period after shortening was active.

I would guess that all speakers use /ʊ/ in these two words; if there are any speakers that use /uː/, that would require some more explanation. It is known that at least some dialects had lengthening of Old English /u/ to Middle English /oː/ in open syllables: this is supposed to be the origin of the Early Modern English pronunciations of above < OE abufan and love < OE lufu with long /uː/ that show up from time to time in poetry. (See "http://english.stackexchange.com/questions/73645".) This could at least explain */wu:d/, if that pronunciation exists. I have no idea how */wu:l/ could be explained, if it exists.