Beat the butter, parsley and garlic together in a bowl. Place a chicken breast on a work surface. Cover with plastic wrap and flatten with a kitchen hammer until about 1/4-inch thick. Repeat with remaining breasts. Place an equal amount of butter in the centre of each breast. Fold the sides of the breasts over the butter, and then roll into a cylinder. Combine the bread crumbs, parmesan, salt and pepper in a shallow dish. Place the flour in a second shallow dish and the egg mixture in a third. Coat the chicken in flour, shaking off the excess. Dip in the egg mixture, evenly coating the chicken. Set in the crumb mixture and coat on all sides. Preheat the oven 350 degrees F. Heat the oil in an oven-proof skillet over medium-high heat. Cook the chicken, seam-side up, until light golden on top. Turn seam-side down and cook in the oven 25-30 minutes, or until cooked through.