I'm still trying to get my head around this. "Tu arrostisci (qualcosa)" would be right, wouldn't it? Usually, "Che cosa ..." followed by the declarative form is right, as in "Che cosa fai?" But that's with 'tu' implied. If you insert tu, is "Che cosa tu fai" wrong? Does it have to be "Che cosa fai tu?"
It's an unusual sentence structure in English. I can only think of two times you'd use it: 1. As a reaction to someone who has said they roast something very strange -- porridge, for instance -- and you react with astonishment or disbelief: You roast WHAT?? 2. A leading question (perhaps to a child): "In the summer, when we have a campfire, we sit around it and roast what?"
To roast meat you surround it with dry heat (usally in an oven) and it cooks by convection. To broil meat it is exposed directly to the heat source (such as an open flame) and cooks by radiation. To fry something it is put in actual contact with the heat (such as a pan, or submerged in hot oil) and it cooks by conduction. Baking is the same as roasting, but roasting usually refers to meat and baking to bread and pastries. Toasting is the same as broiling but again, broiling usually refers to meat and toasting to bread and pastry.
I believe that would be a different verb, just as it is different if you were to say you were roasting because the weather is so hat. http://dictionary.reverso.net/english-italian/roast
Think of it as asking in English, "You there, what are you roasting?" Because in fact, that's how it's spoken in Italian, as if there were a comma and an ever-so-slight pause after the leading word for You--Tu, ... cosa arrostici? Or as if you were going through a kitchen asking each sous-chef what they are doing. "You, what are you chopping? And you, what are you washing? And how about you, what are you roasting?" But in Italian it is used much more frequently than in English, and its use is not limited to the narrow type of questions I used in English. Hopefully this makes sense...