Sprinkle 1/4 teaspoon salt and 1/8 teaspoon pepper over the chicken breasts. In large skillet, heat 2 tablespoons vegetable oil over medium-high heat. Add chicken breasts; brown 2 minutes on each side. Remove to plate; cover.
In same skillet, saute onions and peppers 5 minutes. Stir in creamy Italian salad dressing. Return chicken breasts and any juices to pan.
Cover; reduce heat to medium; simmer for 10 minutes or until an instant-read thermometer inserted in chicken reads 170°F.
Dip 4 boneless, skinless chicken breast halves in 2 beaten eggs, 1/4 cup grated Parmesan, 1 teaspoon Italian seasoning and pinch of red-pepper flakes. Bake at 350°F until cooked through, about 20 minutes.