Working in batches, place 12 mounds (2 tbsp. each) finely grated Parmesan on a silicone baking mat or parchment-lined baking sheet, patting down to form 3-inch rounds. Bake at 400 degrees until golden, 6 to 8 minutes. Using a spatula, quickly transfer each to an inverted 12-cup mini muffin pan. Using your fingers, press down to form cups; let stand to crisp. Mix romaine hearts, Caesar dressing and a pinch pepper. Scoop into baskets.