Learn Spanish (Spain): No cuezas tanto las verduras. - Don't cook the vegetables so long.

Because it is a negative command. When telling someone not to do something (a negative tú command), Spanish uses the present subjunctive form. The infinitive is cocer, which has an o-to-ue stem change. Also, the c changes to z before the letter a to keep the soft "th" sound used in Spain, making it no cuezas.

Since verduras is feminine plural, why doesn't the sentence use tantas?

In this sentence, tanto is an adverb modifying the verb cuezas, meaning "so much" or "so long." Because adverbs describe verbs rather than nouns, they never change their endings to match gender or number. If the sentence meant "Don't cook so many vegetables," it would be an adjective and you would use tantas verduras.

The translation says "cook," so why use cocer instead of cocinar?

While cocinar means "to cook" in a general sense (like preparing an entire meal), cocer specifically means to boil, simmer, or steam something in a liquid. Since vegetables are typically boiled or steamed in water, cocer is the most natural and precise verb to use here.