Preheat the oven to 350 degrees F (175 degrees C). Lightly coat a 13x9-inch baking dish with cooking spray.
Whisk together soup, sour cream, mayonnaise, cream cheese, ranch mix, and cayenne pepper in a large bowl until combined.
Stir in thawed hash browns, shredded chicken, 1 ½ cups shredded Cheddar cheese, ½ cup pepperoncini peppers, and ¼ cup chopped chives until fully combined. Transfer mixture to prepared baking dish and spread evenly. Cover with aluminum foil.
Bake in the preheated oven until heated through, 35 to 40 minutes. Remove from the oven and remove foil.
Stir together mozzarella cheese, potato chips, bacon, remaining ½ cup cheddar cheese, and remaining ¼ cup pepperoncini peppers in a medium bowl. Spread evenly over the casserole.
Continue baking, uncovered, until cheese is melted and topping is lightly browned, 15 to 20 minutes more. Let stand for 5 minutes before serving. Garnish with additional chives.
