Learn French: Quel est ton plat préféré ? - What is your favourite dish?

You must use Quel est (or Quelle / Quels / Quelles) when "What is" is followed by a noun phrase that identifies a specific thing among a group, like ton plat préféré. You would use Qu'est-ce que c'est when asking for a definition, such as asking what a dish actually consists of.

How could I answer this question using the "c'est + invariable adjective" structure from this lesson?

You can state your favorite dish and then describe it generally. For example: La pizza, c'est délicieux ! Even though pizza is feminine, the adjective délicieux stays masculine singular. When you use c'est to give an overall opinion or make a generalization about a concept, the adjective that follows is always invariable.

Why does the adjective "préféré" come after the noun "plat"?

Préféré is technically the past participle of the verb préférer (to prefer) being used as an adjective. In French, adjectives that are derived from verb participles usually go immediately after the noun they modify.

Could I ask "Quelle est ta nourriture préférée ?" instead?

It is grammatically correct but sounds quite unnatural. Un plat refers to a prepared "dish" or "meal," which perfectly captures what we mean in English. La nourriture refers to "food" in a broader, more biological sense—using it in this context sounds a bit like you are asking about a pet's diet!