Preheat the oven to 450 degrees F.
Combine the olive oil, oregano and orange juice in a small bowl. Place the orange halves into a plastic bag. Vigorously stir some salt, pepper and the garlic into the oil mixture until combined. Alternatively, you can use a mortar and pestle to mix the ingredients. Once the mixture resembles a chunky paste, pour half into the bag with the oranges and reserve the other half in the bowl and cover. Place the pork into the bag and marinate for 30 minutes at room temperature.
Transfer the pork to a foil-lined baking sheet sprayed with canola oil. Bake until a thermometer inserted into the pork reaches 140 degrees F for medium-well, 45 minutes.
Let the pork rest as you prepare the buns. Spread some of the mustard onto each sandwich thin, and top with 2 pickle slices, 1 slice ham and 1 slice cheese. Spread about 1 teaspoon of the reserved garlic mixture onto the top sandwich thin. Carve the pork loin into 1/2-inch slices and place 2 slices onto each sandwich. Assemble the sandwiches with the top bread thins.
Place a large nonstick skillet over medium high heat. Spray the pan with canola oil. Place a sandwich in the pan and top with something heavy, like a brick or full kettle of water, to press it down. Cook until the cheese melts, about 2 minutes per side. Repeat with the remaining sandwiches, making sure to re-spray the pan.