Using a mallet, flatten chicken breasts between sheets of waxed paper to a thickness of 3/8". Combine cheese, breadcrumbs and pepper on a separate sheet of waxed paper. In medium bowl, whisk together egg and milk until blended. Dip chicken into egg mixture, then into breadcrumb mixture. Chicken should be thoroughly, but lightly coated. Shake off any excess crumbs. The recipe can be done ahead to this point and refrigerated for up to one hour.
In a large skillet, heat oil (enough to cover pan with 1/4" oil) to medium-high. Add chicken (several pieces at a time) and saute until cooked through and golden brown (about 4-5 minutes per side). Transfer to paper towels and drain. When all of the chicken is cooked, place on a warm platter. Mix melted butter and lemon juice and pour over chicken. Garnish with chopped parsley. 6 servings.