Preheat the oven to 450 degrees . Using paper towels, pat the pork dry; transfer to a large, foil-lined baking sheet. In a small bowl, combine the mustard, EVOO, 2 tsp. coarse salt and 1/2 tsp. pepper; brush generously all over the pork. Roast until the outside is golden-brown and a thermometer inserted into the thickest part of the meat registers 155 degrees , about 30 minutes. Remove from the oven, tent with foil and let rest for 10 minutes. Transfer the meat to a cutting board and thinly slice on an angle.
Arrange 2 to 3 slices of pork on the bottom of each roll; top each with a lettuce leaf. Spread the cut sides of the bun tops generously with mayonnaise and place atop the lettuce.