What have you done? vs What have you been doing?

Interesting question because those two phrases have significantly different connotations. "What have you been doing" is a general question. You might ask this of someone you haven't seen in a while as a conversation starter.
"John, it's good to see you! What have you been doing?"

You could also use it in a specific situation. If you walked into the kitchen and someone has been cooking something you might ask "what are you doing?"

"What have you done" refers to a specific observation and has a negative connotation. If you walk in the kitchen and John is holding a bloody knife and there is a body on the floor you might say "WHAT HAVE YOU DONE??"

You wrote:

If you walked into the kitchen and someone has been cooking something you might ask "what are you doing?"

My question is this:

Would it be equally correct to say, "If you walked into the kitchen and someone has been cooking something you might ask 'what have you been doing?' "

Again, thank you very much for the help.

You could, but that implies something in the past. If they were finished, that would be appropriate.