Combine the garlic, lemon juice, oil and salt in a medium bowl, and whisk to combine. Add the pork shoulder and marinate overnight or up to 24 hours.
Preheat the oven to 350 degrees F.
Roll the pork shoulder into a roast shape and secure with butcher twine, and then wrap in foil. Roast for 3 hours.
Cool the pork completely, then slice into 1/4- to 1/2-inch slices.
Divide the roasted pork evenly among half of the slices of bread. On other slices of bread, layer 3 slices cheese and then 3 slices ham. Place one slice of the pork-topped bread and one slice of the ham-topped bread on a panini press, filling-side up. Close the top of the panini press just over the sandwich, without pressing it, for about 3 minutes. Add some mustard and pickles to the ham, and then close the sandwich. Close the panini press onto the sandwich and press until the outside of the bread is golden and toasted and the inside is warm, about 3 minutes. Repeat for the remaining sandwiches. Slice each sandwich on a diagonal and serve.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Recipe courtesy of David's Cafe Cafecito, Miami, FL