Sprinkle pork with cumin and pepper. Place in a large, plastic resealable bag with garlic and 2 Tbsp. oil. Refrigerate overnight.
Preheat oven to 450°F. Transfer pork to a baking sheet, season with salt and tuck thin end under itself. Roast for 8 minutes. Reduce oven temperature to 350°F and roast for 10 minutes. Let pork cool for about 10 minutes.
Thinly slice pork. Spread 1 Tbsp. mayonnaise on each of 4 sandwich-roll tops; spread 2 tsp. mustard on each of 4 bottoms. Distribute ham, cheese, pork and pickle slices evenly and close sandwiches.
Heat a medium cast-iron skillet or other heavybottomed pan over high heat. In a large skillet or griddle, heat remaining 1 Tbsp. oil over medium-low heat. Place two sandwiches in large skillet. Press preheated medium pan on top to weigh down sandwiches; cook for 10 minutes. Transfer to a plate. Repeat process with remaining sandwiches. Serve with potato salad or chips.