Heat oven to 375° F.
Using a 2-inch round cookie cutter, cut circles from puff pastry and place on a baking sheet. Sprinkle with Parmesan and bake until golden brown, about 18 minutes.
Using your fingers, split each puff. Spread the bottom halves with Dijon mustard and top with salami, lettuce, the peppers, and the top halves of the puffs.