"I am cooking the paprikás, not you."
Translation:Én főzöm a paprikást, nem te.
You need to have "én főzöm" somewhere in your sentence. You're contrasting between the two subjects, so you need én in the focus (right before the verb.)
Another way you can think of it is that "I am cooking it, not you." means exactly the same in English as "It is I who is cooking it, not you." (Unless you mean that "It is it that I'm cooking, not you."! :DD)