Sprinkle some cheese on one half, then beans, then cheese. Use about 1/4 each on each tortilla. (It doesn't have to be precise though!)
Warm a skillet over medium heat. Grease lightly with a little neutral oil like canola or nonstick spray. If using oil, wipe it with a paper towel so there's a very thin coating.
Place two tortillas with fillings on the skillet. After about a minute, fold over the empty side to make a half moon shape. Press down. Add another tortilla or two as you can fit them and repeat to make half moon shapes.
Let each quesadilla cook for 3-4 minutes. Flip and cook for an additional 3-4 minutes.