These sandwiches are packed with vibrant flavors, and with the substitution of roasted potatoes in place of chips or fries, you can still feel satisfied without the guilt.
Preheat oven to 400 degrees. Brush a rimmed baking sheet with oil. Place potatoes at one end and onion at other end; brush vegetables with oil and season with salt and pepper. Bake until potatoes are tender when pierced with a knife and onions are soft and browned, 30 minutes, flipping halfway through.
Meanwhile, in a large cast-iron or heavy skillet, heat oil over medium-high. Season chicken on both sides with salt and pepper. Cook chicken until browned and cooked through, 4 minutes, flipping once. Top each cutlet with 1 slice cheese, cover skillet, and cook until cheese is melted, 1 minute. Layer cutlets on bottom halves of rolls with onion, arugula, and parsley. Spread mayonnaise on top halves of rolls. Sandwich and serve with roasted potatoes.
Thin, flat cutlets are quick-cooking and easy to assemble in sandwiches. You can always substitute pork for the chicken.