。
Have you taken cooking lessons or anything like that?
Literal
Cooking [or-か] something learned-and-such did [question-か]?
Double softening: ~か何か (or something) avoids pinning down exactly what, and ~たりする (do things like X) adds further vagueness. Together they make the question deliberately open-ended — the speaker is asking broadly rather than demanding specifics. Very natural in casual Japanese conversation.