Heat the olive oil in a small heavy-bottomed skillet over medium heat until it shimmers. Add the onion, garlic, and oregano. Cook, stirring frequently, until the vegetables are soft but not brown, about 5 minutes. Add the orange juice and simmer until slightly reduced, about 2 minutes. Season to taste with salt and pepper. Transfer half of the mixture to a medium bowl and reserve the remainder at room temperature. Add the pork chops to the bowl and rub the marinade all over them with your hands. Cover the bowl and place it in the fridge for at least 30 minutes and up to 8 hours.
Heat the vegetable oil in a large heavy-bottomed skillet over high heat until shimmering. Remove the pork chops from the marinade and pat them dry with a paper towel. Add the pork chops to the skillet and cook without moving until well browned, about 2 minutes. Flip the chops, reduce the heat to medium, and continue to cook until the chops register 140 degrees F on an instant-read thermometer, about 4 minutes longer. Transfer the chops to a cutting board, and allow to rest at least 5 minutes.
Heat the oven to 250 degrees F. Split the rolls in half. Spoon the reserved marinade over the cut side of the rolls and spread around with the back of the spoon. Divide the mustard evenly among the rolls, and add a layer of pickles. Slice the pork thinly on a bias and lay the pork slices on top of the pickles. Layer on the ham and cheese and close the sandwiches.
Melt the butter over medium-low heat in a large heavy-bottomed skillet until the foaming subsides. Add two sandwiches and press down firmly with a second skillet. Cook until the bottom bun is crisp, about 5 minutes. Flip the sandwiches, press again, and continue to cook until the second side is crisp and the fillings are heated through, about 5 minutes longer.
Wrap the sandwiches in foil and transfer to the oven to keep warm while heating the other two sandwiches. Serve immediately.
Before starting Food52 with Merrill, I was a food writer and editor at the New York Times. I've written several books, including "Cooking for Mr. Latte" and "The Essential New York Times Cookbook." I played myself in "Julie & Julia" -- hope you didn't blink, or you may have missed the scene! I live in Brooklyn with my husband, Tad, and twins, Walker and Addison.