Preheat the oven to 350°F (175°C) and lightly coat a 9x13-inch baking dish with non-stick cooking spray.
Separate the sliced onion rings and place them in a large mixing bowl.
Sprinkle the onions with garlic powder, Italian seasoning, kosher salt, smoked paprika, black pepper, and cayenne pepper. Toss gently to ensure all rings are evenly coated.
Arrange half of the seasoned onion rings in an even layer across the bottom of the prepared baking dish.
Distribute half of the cubed butter, half of the cheddar cheese, and half of the mozzarella cheese over the first layer of onions.
Repeat the layering process with the remaining onions, followed by the remaining butter, cheddar, and mozzarella. Finish by sprinkling the grated Parmesan cheese evenly over the top.
Cover the dish tightly with aluminum foil and bake in the center of the oven for 30 minutes.
Remove the foil and continue baking for another 30 minutes, or until the onions are tender and the cheese is golden brown and bubbling.
Allow the dish to rest for 5 minutes before serving to let the cheese set slightly.