Mix the bread crumbs and Parmesan cheese on a sheet of wax paper; coat the checken in the mixtue. Heat the oil in a large nonstick skillet over medium heat. Add the chicken and cook until browned and cooked through, about 2 1/2 minutes on each side.
Meanwhile, combine the arugula, tomato, and onion in a medium bowl. Add the dressing and toss to coat.
Place one piece of chicken on each of 4 serving plates. Top each of the cutlets with 3/4 cup arugula salad and ground pepper to taste.
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