In a mixing bowl, combine the black beans, corn, cumin, chili powder, minced garlic, and a pinch of salt. Mash lightly with a fork to help the mixture hold together.
Lay out four tortillas on a clean surface. Sprinkle one-quarter of the cheese over each tortilla, then divide the bean and corn mixture evenly on top of the cheese. Add the remaining cheese and top with the remaining tortillas.
Heat 1 tablespoon of olive oil in a large skillet over medium heat. Cook one quesadilla at a time for 2 to 3 minutes per side until the tortilla is golden and the cheese melts. Add the remaining oil as needed for the rest of the batch.
Let the cooked quesadillas rest for 1 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 form a spiderweb pattern.
Sprinkle the chopped cilantro over the tops before slicing each quesadilla into wedges.