For the pork loin: Preheat the oven to 400 degrees F. Drizzle the oil over the pork and sprinkle liberally with salt and pepper. Transfer the pork to a rack over a heavy-bottomed roasting pan. Roast the pork until a meat thermometer inserted into the thickest part of the loin reads 140 degrees F, about 1 hour. Let the pork rest for 10 minutes, and then reserve 1 1/4 pounds for the sandwich. Slice 1/4-inch thick. Reserve the remaining pork for another recipe.
For the mojo spread: Add the mayonnaise, oil, cilantro, salt, garlic and lime juice to a bowl and stir until evenly combined and spreadable.
For the sandwich: Heat a large, 12-inch cast-iron skillet over medium heat.
Spread the top half of each of the rolls with 2 tablespoons of the mojo spread and 2 teaspoons mustard. Layer the bottom half of the rolls with pork, seasoning it with a pinch of salt. Top with the ham, cheese and pickles. Place the top half of the roll over the bottom half.
Brush the skillet with the butter, place 2 sandwiches in the skillet and brush the top half with butter. Place another cast-iron pan on top of the sandwiches with a heavy can to press down. Alternatively, you can use a panini press. Cook until the bread becomes golden brown on one side, and then flip and repeat on the other side, cooking for 2 to 3 minutes per side. Cook the remaining 2 sandwiches.