Preheat your skillet over medium heat.
Place the black beans between a few layers of paper towels and press down, flattening the beans with your hands. Alternatively, place the beans in a food processor and blend into a paste.
Spread beans across one tortilla in an even layer (you may have a few extra beans).
Top the beans with the shredded cheese, spreading out evenly. Cover cheese with remaining tortilla.
Place butter or oil in skillet and swirl to coat.
Place quesadilla in pan and cook for a few minutes, flip (using a large spatula), and cook a few minutes more, pressing down on it with your spatula. Cook until the tortilla gets some color and the cheese starts to ooze out.
Serve with salsa, guacamole, or both!