Why is ne + plus wrapped around as instead of besoin in the following sentence:
Tu n'as plus besoin de ta voiture.
Shouldn't it be wrapped around besoin as that is the verb word?
Besoin is a noun. The verb is as (from the verb avoir). Avoir besoin is a phrasal verb (literally “to have need”), which determines its meaning, but does not change the grammar. Even if besoin was a verb form, the second negation word would still be after the auxiliary:
Tu ne manges pas tes carottes.
Tu n'a pas mangé tes carottes.