Whisk together the oil with the orange juice, brown sugar, lime juice, garlic, oregano, cumin and salt and pepper in a large mixing bowl. Add tenderloin to the bowl to marinate. Place in the refrigerator for at least an hour, or up to six hours. If desired, pork loin and marinade can be placed into a zipper sealed bag to marinate.
Preheat the oven to 350 degrees.
Melt butter in an oven-safe skillet over high heat. Add pork loin and sear all sides.
Place the skillet with the pork loin in the oven for about 15 minutes, or until the internal temperature reaches 140 degrees. Let pork rest for 5-10 minutes.
Slice pork into ¼ inch slices.
Cover the crust side of each piece of bread with 1 Tablespoon of butter and place on a cutting board.
On the inside of each piece, spread 1 Tablespoon of mustard. For each sandwich, layer 2 slices of the ham, followed by the pickle slices, a slice of the Roasted Cuban pork loin, and cheese on the bottom portions of the sandwich loaves. Add the top half of the bread to finish.
If using a panini maker, press and cook the sandwich on a panini maker following the manufacturer’s recommendations. Sandwich will be golden brown, and the cheese will be melted when finished, about 3-4 minutes depending on your panini maker.
If using a skillet, place one sandwich in a skillet over medium-high heat. Place a second heavy pan, such as a cast-iron skillet, to press down on the sandwich while cooking. Cook for 3-4 minutes per side or until bread is golden brown and cheese is melted. Repeat the process with the remaining sandwiches.