Heat the oven to 425°F. Rub pork with oil, garlic, cumin, salt and pepper and place in a small roasting pan. Roast for 20 to 25 minutes until the thickest part reaches 145°F, then rest for at least 3 minutes and slice thinly.
Lower the oven to 350°F. Split the connected Hawaiian rolls horizontally and place the bottom slab in a parchment-lined 9-by-13-inch pan.
Spread mustard over the bottom. Layer half the Swiss, sliced pork, ham, dry pickles and remaining Swiss, then replace the top slab and press gently.
Brush the tops with butter and cover loosely with foil. Bake for 15 minutes, then uncover for 8 to 10 minutes until the center reaches 165°F.
Rest for 5 minutes and cut into 12 sliders.