OK, a lecture, as requested.
First, it is necessary to repeat that the sentence in the example is egregiously false; in fact, it's a damned lie, derived from another lie. "IQ" is nonsense, doesn't exist, and can't be measured.
So I'm going to substitute a true sentence with the same structure, to avoid spreading noxious nonsense. Instead of measuring, we'll bake, and instead of "IQ", we'll bake pies. On Pi Day, that seems reasonable (sorry; I am informed that Pi day was yesterday, but I doubt it matters to the pies).
- [The one thing we know how to bake best] [is pie].
Second, the grammatical structure of the sentence is that it's a complex sentence, like most English sentences, with [a long complex relative clause as the subject], is as the main verb, and the auxiliary verb, for the predicate noun pie, forming a verb phrase [is pie].
But things have been done to this sentence, and I'll take them apart. I'll put back in the relative pronoun that, taken out because it's not the subject, but rather the object, of bake (best):
- The one thing [(that) we know how to bake best] is pie.
The one thing is a noun phrase modified, defined, and restricted by the [relative clause]. It's there to show the one (uniqueness); otherwise it means the same as the contracted relative what (= the thing which), so this reduces to
- What we know how to bake best is pie.
(Note that best includes the uniqueness of one, so no problem leaving out one.)
And this sentence is a construction called a Wh-Cleft, which is derived by adding a dummy be (here it comes out as is, which is pretty common) in order to separate into two the topical parts of the sentence from an original, simpler statement:
- We know how to bake pie best.
in order to emphasize one part of the sentence (the part after the be in a Wh-cleft); the rest of the sentence goes before the be and is presupposed to be true. I.e, a Wh-cleft
- What we know how to bake is pies.
presupposes that we know how to bake some thing, and asserts that that thing is pies. If you negate the sentence, you can negate pies, but you can't deny our baking knowledge.
- What we know how to bake is not pies.
This is one variety of Cleft sentences in English. There are others.