Preheat a griddle to 325°F or heat a 12-inch skillet over medium heat; if using an oven to toast rolls, preheat the broiler.
Prepare the chicken: cut the chicken breasts into 4 portions and pound each to about 1/4-inch thickness using a meat mallet or rolling pin.
Season both sides of each chicken piece evenly with salt, cracked black pepper, and a light sprinkle of the grated parmesan.
Cook the chicken on the hot griddle or skillet (work in two batches if necessary) until a golden crust forms, about 5–7 minutes per side, flipping once.
When the chicken is almost done, top each piece with a slice of American cheese and let it melt, about 1 minute.
Toast the kaiser rolls: split rolls and spread a light coat of mayonnaise on each cut side; optionally sprinkle each side with about 1/2 teaspoon parmesan. Place cut-side up on a baking sheet and broil 2–3 minutes until golden, watching closely.
Assemble sandwiches by placing one chicken patty with melted cheese on each bottom roll; add lettuce and tomato if desired, then cover with the top roll and serve immediately.
