Rinse the chicken breasts under running water, then place them on a double layer of paper towels and blot them dry. (Be sure to wash your hands well in warm soapy water immediately after handling raw chicken; do the same for any cutting boards or utensils that the meat comes into contact with.)
Place 2 of the chicken breasts inside a large, heavy-duty plastic freezer bag. Partially seal the end of the bag, leaving a slight gap so air can escape. Using the smooth head of a tenderizing mallet or a rolling pin, pound the meat in even strokes, working from the center out (be careful not to tear the plastic), to a uniform thickness of about 1/3 inch. Repeat this process with the remaining chicken in a new plastic bag. Put the pounded cutlets on a plate and set them aside.
Combine the bread crumbs, Parmesan, basil, oregano, salt, and pepper in a shallow medium-size bowl. Stir them to mix. In a separate shallow bowl or pie plate, beat together the egg and milk. Set both of the bowls aside.
Spread the flour on a plate. Arrange the breading ingredients in assembly-line fashion in this order: cutlets, flour, egg mixture, crumb mixture, empty plate. Working one piece at a time, dredge both sides of the cutlet in the flour, knocking off the excess.
Dip both sides of the floured cutlet in the egg mixture.
Coat both sides of the cutlet with the crumb mixture. Set the breaded cutlet on a clean plate and repeat the process with the remaining pieces.
Set a large skillet over medium-high heat and pour in enough olive oil to coat the bottom of the pan, about 2 tablespoons. Heat the oil for 2 to 3 minutes, then add the cutlets. (If your pan isn’t large enough to cook 4 chicken breasts at once, cook them in batches rather than overcrowd the pan.) Fry each side for 2 1/2 to 3 minutes, turning once, until the chicken is browned and cooked through. (To test, make a small cut in the center of the meat; there shouldn’t be any traces of pink.) Remove the cutlets from the heat and serve. Makes 4 servings.
Make the tangy-sweet honey mustard dipping sauce: Stir together 1/4 cup deli-style mustard, 3 tablespoons sour cream, and 1 to 1 1/3 tablespoons honey, to taste.