For the quesadillas, I sautee sliced onion, sliced red bell pepper, and garlic. Then I add salsa,
some spices, such as chili powder, smoked paprika, etc., some lime juice, and the black beans. (I never mash the beans in my burritos or quesadillas - I prefer them whole).
I add one tortilla at a time to a greased skillet, then add extra sharp cheddar, top with some of the bean mixture, fold over until the tortilla is browned on the bottom and cheese is melted. A more typical way is to add the cheese on top, brown the tortilla, then flip it over and brown the other side, but I hate flipping it over - it all falls out! At one point, I may have tried adding the cheese on top, then covering the pan, so the cheese would melt more quickly, but I don't remember. Or you could layer the cheese in the center of the mixture - I never do that, because I use very little cheese, and it would be lost. I've never tried baking them, but that may be a good method.