Preheat grill to medium. Brush pork with oil; season with salt and pepper. Brush grates with oil. Grill pork, flipping once, until cooked through and lightly charred, about 3 minutes; transfer to a plate.
Scoop out soft insides of bread, leaving a 1/8-inch border. Spread mayonnaise and Dijon on opposite halves, then sandwich cheese, pork, ham, and pickles with bread.
Brush oil over both sides of bread. Grill, weighting with a large cast-iron skillet and flipping once, until cheese is melted and bread is lightly marked, 8 to 10 minutes. Transfer to a cutting board; slice into 8 pieces. Serve immediately, with chips.
