Rinse and drain the black beans and corn, finely dice the onion, and mince the garlic cloves.
Pour 1 teaspoon of oil (light olive and avocado oil are my favorites) in a medium skillet, and sauté the diced onion over medium heat until translucent.
Add the minced garlic to the onions and sauté for 1-2 minutes until fragrant. Add the black beans and corn to the skillet, stirring to combine, and heat through. Transfer to a plate lined with a paper towel to soak up the excess moisture. Set aside. Scrape out any food bits from the frying pan.
Dip each corn tortilla in water to moisten both sides. Cook the tortilla in the frying pan over medium heat until soft and pliable, about 30 seconds on each side. Remove from the skillet and repeat for remaining tortillas.
Lay a softened tortilla on a flat surface. Sprinkle shredded cheese evenly over the tortilla. Add a generous spoonful of the sauteed onions, beans and corn mixture. Top with carnitas pulled pork. Fold the tortilla in half.
Return the filled tortilla to the skillet and cook over medium heat until the tortilla is golden brown and the cheese is melted, about 2-3 minutes on each side.
Allow the quesadillas to cool for a few minutes before slicing. Slice each quesadilla into wedges with a pizza cutter and serve warm.