Place pork carnitas in a 3 to 4-quart slow cooker. Cook on High 4 to 5 hours, or on Low for 8 to 10 hours. Remove carnitas from cooker and discard juices. Use tongs or two forks to shred and pull apart the pork.
Heat a comal over medium heat.
On one flour tortilla, spread 1/2 cup of the cheese, followed by 1/3 cup of shredded pork, 1/4 cup of black beans, and 2 tablespoons of chile. Top with additional 1/2 cup of cheese and one more flour tortilla.
Place quesadilla on the comal and cook until the cheese is melted and the tortilla is dark brown and crisp, flipping halfway through, around 6 minutes. Repeat with remaining ingredients. Enjoy immediately.
If you can't find any Queso Oaxaca at your local grocer, you can easily substitute any soft cheese, such as Monterey Jack, Cojack, or Cheddar.