Heat the oven to 325°F and place the pork shoulder in a small covered baking dish.
Whisk the orange juice, lime juice, garlic, cumin, oregano and salt, pour it over the pork and cover the dish tightly.
Roast for 2 1/2 to 3 hours, turning once, until the pork reaches about 195°F and pulls apart with light pressure.
Rest the pork for 10 minutes, shred all of it and moisten it with 1/4 cup of the roasting liquid.
Split the rolls and layer each with mustard, Swiss, ham, warm roast pork, pickle slices and a second slice of Swiss.
Close the sandwiches, spread the exteriors with butter and place them in a preheated sandwich press or heavy skillet over medium heat.
Press for 3 to 4 minutes per side, weighting skillet sandwiches with a second pan, until deeply crisp and the center reaches 165°F.
Cut each Cubano diagonally into 2 halves and serve immediately.