Combine all of the roast pork ingredients except for the pork butt in a food processor until smooth.

Pierce the pork with a sharp knife several times on each side.

Place the pork into a bowl and cover it with the marinade.

Wrap the bowl with plastic wrap and place it in the refrigerator for at least 8 hours or up to 24.

Preheat the oven to 325 F and line a roasting pan with foil.

Remove the pork from the marinade and place it on the pan.

Cover the pan with foil and bake for 2 ½ hours.

Remove the foil and raise the oven temperature to 425 F.

Cook the pork for an additional 1 ½ hours, until the pork is tender and the internal temperature has reached 150 F.

Cover and set the pork aside to cool, then slice it into ¼-inch slices.

Spread a tablespoon of butter over the top and bottom of each loaf of bread and 1 tablespoon of mustard over the top piece.

On the bottom piece, layer a quarter of each of the following ingredients in order: roast pork, pickle, ham, and Swiss cheese, and finish with the top piece of bread, mustard-side down. You should have butter on the outside of both halves of the assembled sandwich.

Place the sandwich in a panini press or a preheated cast-iron skillet with a heavy lid to press down the top.

Cook the sandwiches for 6 minutes (or 3 minutes per side if using the cast-iron pan method) until the bread is golden brown and the cheese has melted. Repeat with the remaining sandwiches.

Cut the sandwiches in half on a bias and serve with your favorite chips.