Butterfly chicken breasts by making a lengthwise cut horizontally through breasts to within 1/2 inch of other side. Open breasts, and sprinkle evenly with sliced basil; place between 2 sheets of heavy-duty plastic wrap. Flatten chicken to 1/2-inch thickness using a cast-iron skillet or meat mallet.
Stir together mayonnaise, milk, garlic, 2 teaspoons pepper, and 1 teaspoon salt in a shallow dish; add chicken. Cover and chill at least 4 hours or up to 24 hours.
Cook bacon slices in a large cast-iron skillet until crisp; remove bacon, and drain on paper towels, reserving drippings in skillet. Crumble bacon, and set aside. Add oil to drippings in skillet, and heat to 350°, stirring and scraping to release browned bits from bottom of skillet.
Combine flour, remaining 2 teaspoons black pepper, and remaining 1 teaspoon salt in a shallow dish. Remove chicken from marinade, discarding marinade. Scrape and discard excess marinade from chicken. Dredge chicken in flour mixture. Fry 2 to 3 minutes on each side or until golden brown and chicken is done.
Divide lettuce evenly between each of 2 serving plates. Top each with 1 cup melon, and drizzle with desired amount of Honey-Mustard Dressing. Cut chicken into thin slices, and place evenly on top of melon. Sprinkle with bacon, and garnish, if desired. Serve immediately.