Preheat the oven to 425°F (235°C). Line a sheet pan with foil.

Marinate pork: Whisk all of the pork ingredients (except tenderloin) in a bowl until fully combined. Add the tenderloin, tossing to coat. Cover in plastic and let marinate on the counter for 30 minutes.

Roast pork: Transfer the tenderloin to the prepared sheet pan and pour the marinade over top. Roast until the pork has reached an internal temperature of 140°F (60°C) on an instant-read thermometer inserted into the center, about 20 to 25 minutes. While the pork is roasting, prep sandwiches.

Finish pork: Once the pork is cooked, transfer to a cutting board and let rest for 5 minutes, then carve into ¼-inch slices on a bias.

Heat a panini press or pan on medium heat. Rub the outer side of the top and bottom of each loaf with the softened butter and arrange, butter-side down, on a cutting board. Spread yellow mustard on the inside of each piece of bread. On the bottom half of each loaf, layer the pickles, followed by roast pork, ham, and cheese. Season with a pinch of salt and close with the top half of the bread. Repeat with the remaining loaves and fixings.

Grill sandwiches: Working in batches, press the sandwiches in the panini grill or cook in the pan with another pan on top until golden brown and the cheese has melted, about 6 to 10 minutes.

Transfer to a board and cut each one in half on a bias.