In a large bowl, whisk together the Italian dressing, Worcestershire sauce, Italian seasoning, garlic powder, onion powder, chili powder, salt, and pepper.
Pound each chicken breast to about 1/2-inch thickness using a meat mallet or rolling pin, then add the chicken to the marinade, coating each piece. Cover and refrigerate for at least 2 hours or up to 24 hours.
Heat a thin layer of oil in a large nonstick skillet over medium-high heat. Cook the marinated chicken breasts 6–7 minutes per side, or until cooked through and internal temperature reaches 165°F (74°C).
While the chicken cooks, combine the shredded mozzarella, shredded Parmesan, and ranch dressing in a medium bowl to make the cheese topping.
In a small bowl, mix the Panko breadcrumbs and melted butter until evenly coated.
Top each cooked chicken breast evenly with the cheese mixture, then sprinkle the buttery Panko on top. Place the chicken on a broiler-safe sheet or skillet and broil 3–4 minutes, watching closely, until the cheese is melted and the Panko is golden and crisp.
Remove from the oven and let rest briefly before serving.