Heat a non-stick skillet over high heat. Add the vegetable oil and heat until shimmering. Add the pork carnitas and cook without stirring for 2-3 minutes, allowing the edges to crisp. The pork does not need to be fully heated through as it will continue to warm during quesadilla assembly. Remove the pork from the skillet and set it aside.

Reduce the heat to medium. Add half of the butter to the skillet, allowing it to melt and coat the surface evenly. Once melted, sprinkle approximately 1 tablespoon of the shredded cheese directly onto the skillet to create a golden, crispy cheese crust.

Place one flour tortilla directly on the buttered and cheesed skillet. Evenly distribute half the remaining shredded cheese over the tortilla, followed by half the black beans and half of the crisped pork carnitas. Sprinkle another small amount of cheese on top before folding the tortilla in half.

Allow the quesadilla to cook for 5-6 minutes, or until the bottom is golden brown and the cheese has fully melted. Flip carefully and cook the other side for an additional 2-3 minutes, ensuring a golden, crispy exterior.

Repeat steps 2 through 4 using the second tortilla and the remaining ingredients.

Slice the quesadillas into wedges and serve immediately with your preferred toppings such as sour cream, guacamole, and pico de gallo.