For the pork:
- Preheat oven, grill or pellet smoker to 300 degrees.
- Slice the pork into 2-inch chunks and trim off excess fat. Arrange in an ovenproof pan or Dutch oven and top with zest, onion, garlic and bay leaf. In a mixing bowl combine the beer, stock, salt, oregano, pepper and cumin. Pour the mixture over the pork and add water to cover the meat by one inch.
- Place the pan on the stovetop on medium-high and bring to a simmer. Place the pan in the oven, grill or pellet smoker until it becomes tender and falls apart, 1½-2½ hours (add hot water if needed to keep covered).
- Remove zest and bay leafs, pour off most of the braising liquid, and shred with a fork. Set aside.
For the quesadillas:
- Lay out eight tortillas on a sheet tray. Place a 1/4 cup of cheese on each tortilla. Top them with the shredded pork, a few tablespoons of onions, chiles to taste, another 1/4 cup of cheese and then the second tortilla.
- Heat a grill to medium direct heat. You can also use a grill pan or cast iron skillet.
- Brush the grill with a little oil and place the quesadillas on the grill. Cook on both sides until the tortilla gets crisp and cheese is melted.
Cut the quesadillas into wedges and serve with crema, salsa and limes on the side.