In a course of philosophy I heard “I mean it’s not like you’re going to fall asleep already, riddle me that”. My dictionary gives me only the noun’s signification “mystery”. but I guess it is used her as a verb. It’s mean something like “make that mysterious”?
Riddle me that is an idiom that means: Go ahead and try to explain that to me.
It trades upon the secondary meaning of riddle which is to solve or explain a riddle to someone. Link to definition here.
So essentially when someone says "Riddle me that (or this)" they are saying:
I find the statement I just made to be puzzling to the point where I consider it to be a riddle. Go ahead and try to explain it to me.
When someone says that, they typically don't expect an answer to be easily forthcoming.