Place the black beans in a mixing bowl and mash them with a fork until most are broken down. Stir in the cumin, chili powder, and salt until evenly mixed.
Lay out four tortillas on a clean surface. Spread the bean mixture evenly over each one, then sprinkle the cheese on top. Cover with the remaining four tortillas to form quesadillas.
Heat 1 tablespoon of vegetable oil in a large skillet over medium heat. Cook two quesadillas at a time for 2 to 3 minutes per side until the tortillas turn golden and the cheese melts. Repeat with the remaining oil and quesadillas.
Transfer the cooked quesadillas to a cutting board. 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 a web pattern.
Cut each quesadilla into four triangles and arrange them on a serving plate.