Preheat grill to 400 degrees F using direct heat.
Slice each loaf of Cuban bread in half, creating 4 separate sliced loaves.
Assemble sandwiches by spreading mustard on one side of the bread and the cilantro-garlic aioli on the other side.
Place about 1 lb. of mojo braised pork on each slice of bread with mustard.
Top mojo pork with 3 slices of deli ham, 2 to 3 slices of Swiss cheese, and 1 dill pickle sandwich slice.
Top with bread spread with cilantro-garlic aioli.
Place a large cast iron pan on the grill and add 2 Tbsp. butter to cast iron.
In 4 separate batches, place each sandwich in pan and press down with lightly with another cast iron pan or metal spatula, browning and slightly flattening bread and melting the cheese, about 2 minutes on each side.
Wipe out cast iron pan with paper towel after each sandwich and repeat until all sandwiches have been made.
Slice warm sandwiches into desired sizes and serve with a side of cilantro-aioli.