Preheat oven to 375°F (190°C) and grease a 9×13-inch dish.
Cook ground beef with onions, garlic, and bell peppers until browned; season with salt, pepper, and paprika.
Mix cream of mushroom soup, sour cream, cream cheese, beef broth, and Worcestershire sauce until smooth.
Layer half of potatoes in dish, add beef mixture, pour half of sauce, and sprinkle 1 cup cheddar cheese.
Add remaining potatoes, top with remaining sauce, cover with foil, and bake 45 minutes. Remove foil, add remaining cheeses, and bake uncovered 15-20 minutes until golden. Rest 10 minutes before serving.
Notes
For a richer flavor, use full-fat cheese and cream.