In a bowl, combine the orange juice, lime juice, minced garlic, cumin, oregano, cayenne pepper, kosher salt, and black pepper. Mix well.
Place the pork shoulder in the slow cooker, the fat side should be facing up.. Pour the marinade over the pork, ensuring it is well coated. Cook on low heat for 8-10 hours, or until the pork is tender and easily shreds with a fork.
Once cooked, remove the pork from the slow cooker and discard any fat and skim, if your pork has bones remove and discard them. Shred the pork using two forks and return the shredded pork to the slow cooker to soak up the flavorful cooking juices. Set aside.
For the Cubans:
If using a panini press, preheat it to medium heat. If using a cast iron skillet, place it over medium heat.
Trim the ends off of each loaf of bread and cut the loaves in half horizontally.
Spread a thin layer of the softened butter on the outside of each slice of bread. On the inside of the bread, spread a generous amount of yellow mustard.
On the bottom halves of the bread, layer the swiss cheese, sliced ham, shredded pork, pickles and then another layer of swiss cheese, finally place the top half of the bread on the sandwiches. Repeat until all the sandwiches have been assembled.
(If using a panini press) Place the sandwiches in the preheated panini press and close the lid. Grill for 3-5 minutes, or until the bread is golden brown and crispy, and the cheese is melted. Repeat with the remaining sandwiches.
(If using a cast iron skillet) Place the sandwich into the preheated skillet. Use another heavy skillet or a foil-wrapped brick to press down the sandwich. Cook for 2-3 minutes on each side, pressing down firmly, until the bread is golden brown and crispy and the cheese has melted. Repeat with the remaining sandwiches.
Slice the sandwiches in half and serve, enjoy with a side of chips or a fresh salad and additional pickles. Enjoy!
Notes
Store leftover shredded pork in an airtight container in the refrigerator for up to 3-4 days. To reheat, warm in a saucepan over medium heat or in the microwave.
Store leftover assembled sandwiches in the refrigerator for up to 2 days wrapped tightly in foil. Reheat in a skillet or oven until warmed through.
If Cuban bread is unavailable, Italian bread or even french bread can be used as a substitute.
Add more or less of the cayenne pepper depending on your spice preferences or even leave it out all together.
For an added layer of flavor, consider including slices of genoa salami to your sandwich. Layer it between the ham and shredded. The genoa salami is added to the Tampa Florida version of the cuban, whereas the Southern Florida version leaves it out.