So I start with two white corn tortillas and some no-stick spray on the skillet.
Lay one tortilla in the sprayed pan and warm a bit. Sprinkle some cheddar around the outside of the tortilla, in a ring around the edge, to hold the egg in place. Once the cheese has melted a bit, break an egg into the middle.
Let the egg cook a bit (1-2 minutes), sprinkle a litle more cheese over the egg and then place another tortilla on top; then flip the quesadilla.
Once both sides are browned and the egg is the desired "doneness," it's ready to go. (I have returned a quesadilla or two to the pan upon learning it was too gooey for my taste. I like my egg a bit runny, but not too runny... a bit of a science to it, but I've learned as I've gone along.)
One hand on the quesadilla, one hand on the camera, here we go! You get the idea, right? Yum.
A quick Google search only returned scrambled egg quesadillas. Hmm. No so much. That's a bit too much like a breakfast burrito... fine in it's own way, but no fried egg quesadilla! Do you think I might have actually invented something? That would make my day. Especially since it's something that's so yummy, I think I ate it almost every night for a week not that long ago... sad but true. I have yet to talk my nightly dinner companions into it, they look at me a little like I'm headed for the Cocoapuffs, but maybe one of these days...