Can one use embellishing as an adjective? For example, “He gave an embellishing speech.”
ODO on embellish:
verb [with object]
make (something) more attractive by the addition of decorative details or features:
blue silk embellished with golden embroidery
• make (a statement or story) more interesting by adding extra details that are often untrue:
followers often embellish stories about their heroes
So an action can grammatically be "embellishing", but it's unlikely that the agent would be a speech. The agent must be an embellishment.
He gave the story some embellishing details to enhance his reputation.
[I suppose it's possible that a speech might embellish something, but it's difficult to think of an example.]
Although FreeDictionary searches for defining and stirring show both being given as headwords and labelled as adjectives, embellishing is only mentioned as an inflection of the verb embellish.
This indicates that, although one would be very hard pushed to find a rule forbidding the use of the -ing forms of some verbs as participial adjectives, caution might well be advised so as to avoid distinctly odd sounding pairings. The Google Ngram seen here shows that a moving speech and a stirring speech are quite acceptable whereas an embellishing speech and a praising speech are seldom if ever encountered.
The OED has an entry for the adjective embellishing, which is defined as ‘that embellishes or beautifies.’ There are only two citations, one form the sixteenth century and one from the seventeenth. If used in your example, it could refer only to the subject of the speech, and not to the speech itself. It is unlikely to be used much as an adjective at all now, and is probably best avoided.
"Embellishing" could be applied to a word or phrase, but I've never seen it done.
Edit: I realize from a comment there was a use/mention confusion here. "Embellishing" could be applied to a word or phrase that refers to a word or phrase. For example:
His speech was full of embellishing turns of speech.
It's my experience that the use of embellishing clichés has the opposite of the intended effect.
Those are grammatically correct and comprehensible, but as I say, I've never seen a sentence like that in the wild.
Why not ? You may embellish a story of your accomplishments, the narration of your life, which are the contents of your speech, but even your style, that is your speech itself.