Start by combining orange juice, lime juice, garlic, onion, oregano, cumin, salt, and pepper. Mix everything well so the flavors blend evenly. This marinade is key to giving the pork its signature Cuban taste.
Place the pork shoulder into the slow cooker and pour the marinade over it. Cover and cook on low for about 8 hours or until the meat is fork-tender. The pork should easily shred and soak up all the citrusy flavors.
Once the pork is cooked, remove it and shred it using two forks. Return the shredded meat to the slow cooker and mix it with the juices. This keeps it moist and flavorful.
Slice the bread and spread mustard on each side. Layer with shredded pork, ham, Swiss cheese, and pickles. Make sure each bite has a bit of everything for the best flavor balance.
Butter the outside of the bread and place it in a skillet or panini press. Cook until the bread is golden and crispy and the cheese is melted. Press slightly to get that classic Cuban sandwich texture.