Learn Dutch: De boon is niet bitter, de spruit evenmin. - The bean is not bitter, nor is the sprout.

The second half of this sentence is shortened to avoid repetition. The full thought is de spruit is evenmin bitter (the sprout is neither bitter / also not bitter). When you drop the repeated verb and adjective, you are just left with the subject and the adverb, resulting in de spruit evenmin.

If I wanted to include the verb in the second part, what would the word order be?

If you start the second clause with the adverbial conjunction evenmin, it triggers inversion (verb before subject), just like most other adverbs at the start of a clause. The full version would be: De boon is niet bitter, evenmin is de spruit bitter.

Could I just use ook niet instead of evenmin?

Absolutely. You could say ..., en de spruit ook niet (and the sprout also not). Evenmin means exactly the same thing but packages "also not" or "neither" into a single, slightly more formal word. It is very common in written Dutch and higher-level speech.

I usually see Brussels sprouts translated as spruitjes. Why is it just spruit here?

You are right that Brussels sprouts are almost always called spruitjes (plural diminutive) when they are served as a meal. Using the singular, non-diminutive spruit here treats it as a general botanical category to perfectly match the singular de boon.