Best Ever Cuban Sandwich

Prepare pork shoulder: Add onion, garlic, orange juice, lime juice, cumin, oregano, black pepper, and salt into a food processor or blender and process until smooth.

Place pork in the bottom of a heavy-bottomed Dutch oven or large baking dish and cut 3 or 4 large deep slits in the meat.  Pour marinade over pork, cover, and marinate in the refrigerator 4 hours or overnight.

Place Dutch oven with prepared pork, covered, in the oven and set the temperature to 325 degrees F (165 degrees C). Bake until pork is very tender, 3 to 4 hours. Remove from the oven; rest 15 minutes. Remove pork to a cutting board. Skim any fat from the cooking liquid, and set cooking liquid aside.

Shred pork with two forks, and discard any remaining fat and bone. Return pork to the pot, and add cooking liquid back into meat as needed to moisten.

Preheat the oven to 375 degrees F (190 degrees C).  Heat a large skillet over medium heat.

Spread about 2 tablespoons softened butter over cut sides of bread and place bread, buttered sides down, in skillet. Cook until buttered side is lightly browned and toasted, about 3 minutes.

Stir mustard and mayonnaise together in a small bowl. Spread about 2 teaspoons mustard mixture over bottom halves of bread and top with 1 slice of cheese, tearing as needed to fit the bread without hanging over the edges. Using tongs or a slotted spoon, add about 1/2 cup shredded pork to each sandwich, draining off any excess liquid. Top each evenly with ham, 3 pickle slices, and 1 cheese slice. Spread remaining mustard mixture evenly over top pieces of bread and place on top.

Reheat the skillet over medium heat. Spread about 1 tablespoon butter lightly on the outsides of the 4 bottom buns. Working 2 sandwiches at a time, place sandwiches, buttered side down, in skillet. Place 1 or 2 heavy-bottomed skillets on top of sandwiches to weigh them down. Cook until toasted and lightly golden brown, 2 to 3 minutes. Remove weighted skillets.

Spread remaining 1 tablespoon butter over the 4 top halves of sandwiches, flip and press with weighted skillets again until toasted. Remove the first 2 sandwiches from skillet; repeat the toasting process with remaining sandwiches. Cut sandwiches in halves and serve immediately.