Prepare the chicken for dredging. On a dinner plate, combine the flour, salt and pepper. In a wide shallow bowl beat the egg with 1 Tbsp water. On another dinner plate combine the breadcrumbs and parmesan cheese.
Coat the chicken cutlets on both sides with the flour mixture, dusting off the excess, then dip both sides into the egg mixture, and finally dredge both sides in the breadcrumb mixture, pressing lightly.
Heat the butter and olive oil in a cast iron skillet over medium low heat and cook 2 chicken cutlets at a time for 2-3 minutes on each side, until just cooked through. Remove the cooked chicken to rest on a sheet pan.
Top each chicken cutlet with fresh mozzarella and place under the broiler for about 2 minutes or until cheese is melted and golden brown.
Serve with homemade roasted tomato marinara sauce over pasta.