Place each chicken breast on a cutting board and use a sharp knife to cut them horizontally almost in half, leaving one edge intact. Open them like a book so they are evenly thin.
In a small bowl, mix the softened butter with the chopped parsley, minced garlic, and lemon-pepper seasoning. Ensure the mixture is smooth and well-blended.
Place about 1 1/2 tablespoons of the herb butter in the center of each opened chicken breast. Fold the chicken over the butter and press the edges firmly to seal in the filling.
Dredge each stuffed chicken breast in the flour first (shake off excess), then dip in the egg, and finally coat evenly with the breadcrumbs.