In a bowl, lightly mash the black beans with a fork, leaving some whole. Stir in the corn, cumin, chili powder, garlic powder, and salsa.
Lay out half the tortillas. Sprinkle each with a little cheese, spread with the bean mixture, and top with more cheese and a second tortilla.
Heat a large skillet over medium heat and brush lightly with oil.
Cook each quesadilla for 2–3 minutes per side, pressing gently with a spatula, until golden and the cheese is melted.
Let rest 1 minute, cut into wedges, and serve with sour cream, guacamole, or salsa.