Preheat the grill. Turn on your grill to medium heat and close the lid. Allow the grill to preheat while you butter the cut sides of your bread.
Heat the pork. In a large sauté pan, combine the pork, orange juice, lime zest and juice, oregano, red pepper flakes, cumin, onion powder, salt and black pepper.
Warm over medium heat until the sauce is evenly distributed throughout the pork and everything is warmed through.
Step 2: Assemble The Sandwiches
Assemble the sandwiches. Layer the mustard, pickles, cheese, ham, and pork across the toasted sides of the bread.
Press the halves of the bread together and wrap as tightly as you can with the foil.
Step 3: Grill the Cuban Sandwiches.
Place the foiled sandwich on the grill and top with the heavy, preheated pan.
Turn the temperature of your grill down to low and let the sandwich get all toasty and the cheese melted.
Check the sandwich after about 10 minutes.
Cool and serve. Allow the sandwich to cool for 5-10 minutes before slicing into individual servings. Top with chopped cilantro.