How does the grammar work behind "How [adjective] [subject] [verb] [object]"?

Solution 1:

How detestable I find those insects, how pleasant the noises they make when I crush them....

The sentence as written is put together very well. But something has been omitted from it: I find (not are.) This omission of words/ phrases from sentences that ain't "necessary" is quite common in the English language. In fact, there's a generic name for such omissions of words and phrases from sentences: Ellipsis. It is further subdivided into lots more types (in this case, the subtype being Gapping.)

A fuller version of the sentence might look like this:

How detestable I find those insects, how pleasant (I find) the noises they make when I crush them. It is strange, truly; I despise the silence of their absence more.

As you can see, the sentence has perfect parallelism as well:

How [adj.] I find [NP], how [adj.] (elided phrase) [NP]...

Actually, by thrusting are into the sentence, you're making it ungrammatical.