Place the black beans in a mixing bowl and mash them with a fork until most are broken down but some chunks remain. Stir in the cumin, chili powder, garlic powder, salt, and pepper.
Lay one tortilla flat and spread one quarter of the bean mixture over half of it. Sprinkle one quarter of the cheese on top of the beans. Fold the tortilla in half to close.
Heat 1/2 tablespoon of olive oil in a large skillet over medium heat. Place one folded tortilla in the skillet and cook for 2 to 3 minutes until the bottom is golden. Flip and cook the other side until the cheese melts and the tortilla is crisp. Repeat with the remaining tortillas, adding oil as needed.
Let the cooked quesadillas rest for one minute. Spoon the sour cream into a small zip-top bag, snip off one corner, and pipe concentric circles on each quesadilla. Drag a knife from the center outward in several lines to create the spiderweb pattern.