A Cuban sandwich combines citrusy, tender roast pork with sliced ham, mayonnaise, mustard, Swiss cheese and pickles, which are then pressed on a baguette until the buttery bread is golden and crisp.
In a blender add the olive oil, garlic, cilantro, orange zest, orange juice, lime zest, lime juice, vinegar, oregano, cumin salt and pepper, and pulse to combine.
Put the pork in a re-sealable 1-gallon plastic bag; add the marinade and close, removing any air. Refrigerate for at least 6 hours and up to 24 hours.
Preheat the oven to 425ºF (220ºC). Let the pork come to room temperature. Place a rack in a roasting pan and add the meat. Roast for 20 minutes then lower the temperature to 325ºF (170ºC). Continue to roast until a thermometer inserted into the middle of the roast reads 185ºF (85ºC), about 4 hours.
Let the meat rest for about 30 minutes before slicing. Thinly slice the pork and set aside.
For the Cuban sandwiches:
Slice the bread in half so you now have 4 rolls, then slice each piece in half lengthwise. Spread mayonnaise on the bottom of each sandwich and mustard on the top half of each sandwich. To assemble the sandwich, layer 3 slices of the roast pork followed by slices of ham, Swiss cheese, and pickles.
Close the sandwich and spread butter on the Panini press and on the top of the bread. If using a skillet, heat over medium heat, add butter and allow to melt. Add the Cuban and the other skillet as a weight on top. Press the sandwich until the cheese is melted and the bread is golden brown, about 4 minutes each side.
Remove and cut the sandwich in half on a 45º diagonal. Serve immediately with extra pickles on the side.