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, and salt until evenly combined.

Lay four tortillas on a work surface. Spread the bean mixture evenly over each one, then sprinkle the shredded cheddar cheese on top. Cover with the remaining four tortillas to form quesadillas.

Heat the olive oil in a large skillet over medium heat. Cook each quesadilla for 2 to 3 minutes per side until the tortillas turn golden and the cheese melts. Work in batches if needed to avoid crowding the pan.

Transfer the cooked quesadillas to a cutting board. Spoon the sour cream into a 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 web pattern. Slice and serve.