Preheat oven to 400°F Place a chicken breast, skinned-side down, on a cutting board. Keeping the blade of a sharp knife parallel to the board, make a horizontal slit along the thinner, long edge of the breast, cutting nearly through to the opposite side. Open the breast so it forms two flaps, hinged at the center. Place a slice of cheese on one flap, leaving a 1/2-inch border at the edge. Press remaining flap down firmly over the cheese and set aside. Repeat with the remaining breasts.
Lightly beat egg whites with a fork in a medium bowl. Mix breadcrumbs, Parmesan, parsley, salt and pepper in a shallow dish. Holding a stuffed breast together firmly, dip it in the egg whites and then roll in the breadcrumbs. Repeat with the remaining breasts.
Heat oil in a large ovenproof skillet over medium-high heat. Add the stuffed breasts and cook until browned on one side, about 2 minutes. Turn the breasts over and place the skillet in the oven.
Bake the chicken until no longer pink in the center, about 20 minutes. Serve with lemon wedges.