Cut the pork tenderloin in half crosswise with a sharp knife, creating two 5-inch-long pieces. Make a vertical cut down the middle of each piece, about 3/4 of the way through. Open the pieces like a book. Lay them cut-side down on a piece of plastic wrap, cover with another piece and use a meat mallet to lightly pound the pork to about 1/2 inch thick.
Add the pork, 1/4 cup of the yellow mustard, olive oil, pickle brine and garlic to a quart- or gallon-size resealable bag. Close the bag, and rub the marinade into the pork. Let sit at room temperature for 30 minutes.
Meanwhile, prepare a grill or large grill pan for medium-high heat.
Once the pork has marinated for 30 minutes, transfer it to a plate, shaking off any excess marinade. Lightly oil the grill grates with vegetable oil. Sprinkle both sides of the pork liberally with salt and pepper, and grill until charred on both sides, 4 to 5 minutes per side for medium doneness. Transfer the pork a cutting board, and let it rest for 5 minutes. Reduce the grill heat to medium. Slice the pork across the grain into 1/8-inch-thick slices, and season lightly with salt and pepper.
Brush the outside of the Cuban loaf with the butter, and lay the loaf halves cut-side up on a very long piece of aluminum foil. Mix the remaining tablespoon yellow mustard with the mayonnaise, and slather the mixture onto both pieces of bread. Layer the ham, pickles, pork and Swiss cheese on one half of the bread. Top with the other half, and wrap the sandwich up in the foil.
Put the sandwich on the grill, place a large baking sheet on top and weigh it down with a large cast-iron pan or 2 large cans of food. Grill for 5 minutes, remove the baking sheet and weight, flip the sandwich, weigh it down again and grill until the Swiss cheese has melted, about 5 minutes more.
Unwrap the sandwich, cut into 4 pieces and serve immediately.
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