Preheat the oven to 350°F (175°C).
Butterfly the chicken breasts all the way through so you have 4–6 thinner chicken pieces.
Spread the sliced red onion across the bottom of a 9×13-inch baking dish. Drizzle with olive oil and sprinkle with about one-quarter of the ranch seasoning. Toss to coat, then arrange the onions in an even layer.
Place the chicken pieces in a single layer over the onions. Sprinkle the remaining ranch seasoning evenly over the chicken.
Spoon the barbecue sauce over the chicken, using approximately ¼ cup per whole chicken breast and dividing it between the butterflied pieces.
Arrange 3–4 pepperoncini slices over each chicken piece. Drizzle 1 teaspoon of pepperoncini juice across the entire baking dish.
Sprinkle the freshly shredded mozzarella evenly over the chicken.
Place the French fried onions in a large zip-top bag and gently crush them into rustic pieces. Add the melted butter, seal the bag, and shake until the onions are evenly coated.
Sprinkle the buttery fried onions evenly over the mozzarella.
Cover the baking dish tightly with aluminum foil, crimping the foil securely around the edges. This traps moisture inside and helps keep the chicken tender while it cooks.
Bake the Mississippi Mud Chicken Bake covered for 25 minutes.
Carefully remove the foil and bake uncovered for another 10–15 minutes, until the cheese is bubbling, the onion topping is golden, and the chicken is completely cooked.
Check the thickest portion of the chicken with an instant-read thermometer. It should reach 165°F (74°C).
Rest for about 5 minutes before serving.