In a large non-stick skillet over medium-high heat, warm the shredded pork until it's slightly crisped, about 2-3 minutes.
Remove the pork from the skillet and set aside. Reduce heat to medium.
Melt half the butter in the skillet, swirling to coat the surface. Place one tortilla in the skillet and sprinkle half the cheese over it.
Add half the black beans and half the crisped pork on top of the cheese. Cook for 5-6 minutes until the cheese is melted and the tortilla is golden brown.
Fold the tortilla in half to form the quesadilla. Remove from skillet and keep warm. Repeat with the remaining ingredients for the second quesadilla.
Cut each quesadilla in half and serve hot with optional sides like sour cream, guacamole, Pico de Gallo, shredded lettuce, or corn salsa.