Combine the first 6 ingredients in a bowl. Add the pork and turn to coat. Cover, refrigerate and marinate for 2 to 4 hours.
Preheat your barbecue to medium heat. Roll the pork in the marinade to coat it in it. Set pork on the grill and season with salt and pepper. Close the lid and grill pork 12 to 15 minutes, turning occasionally, or until just cooked through.
Cool pork to room temperature, and then cut into thin slices. Now cut those slices into thin strips and set in a clean bowl. Toss in the cheese, jalapeño and cilantro.
Preheat the oven to 200 degrees F. Set a large, non-stick skillet over medium heat. Place an equal amount of pork mixture on one half of each tortilla. Fold each tortilla into a half-moon shape. Cook 2 stuffed tortillas 3 minutes per side, or until the cheese is melted and the tortillas golden brown. Set the cooked quesadillas on a baking sheet and keep warm in the oven while you cook the last 2. Cut each quesadilla into 4 wedges and arrange on a platter. Serve with salsa and sour cream for dipping.