Why does "du" come between the verb and the thing that is being cooked? I thought "lagar mat" stuck together. Why not "hur lagar mat du?"
The subject comes between in sentences like these, both for objects, particles, and prepositions. The subject needs to be there, right after the verb, and even particles (like om in tycka om) are separated from the verb.
What Arnauti said, but as an extension, it would literally translate as 'How do you make food' so the hur larger du is the how do you make, and the food is thing you are making.
Does this mean "you" as in a person- how do YOU cook, person I am talking to- or a general "you" like the french "on"- how does one cook?
A person. For general you (like French "on") Swedish uses the pronoun man.
How would you say "How do you cook your meat?". I thought the "du mat" might have made it so. Thanks!
Could you just leave out mat, and you could assume that a person meant cooking food, like it translates into English?
No, because "lagar" doesn't always mean "cook". It's more like "How do you fix food?" or "How do you prepare food?"
See the answer of Aebleskiver59. "Jag lagar mat" means "I'm cooking". "Hon lagar fisken" means " She is cooking the fish".