Preheat Oven: Set your oven to 375°F (190°C) and lightly grease a 9×13-inch baking dish with cooking spray or olive oil.
Cook Ground Beef: In a large skillet, heat the olive oil over medium heat. Add the ground beef and cook, breaking it apart with a spoon, until browned and fully cooked, approximately 5-7 minutes. Drain any excess fat if necessary.
Add Aromatics: Incorporate the chopped onion and minced garlic into the skillet with the beef. Continue cooking for an additional 3-4 minutes until the onion becomes soft and translucent.
Season the Mixture: Stir in the dried Italian seasoning, paprika, salt, and pepper. Mix thoroughly to ensure the beef is evenly seasoned.
Assemble the Casserole: Arrange half of the thinly sliced potatoes at the bottom of the prepared baking dish. Spread the cooked ground beef mixture evenly over the potatoes. Layer the remaining potato slices on top of the beef mixture.
Add Liquid: Pour the beef broth (and milk, if using) over the layered mixture to provide moisture during baking.
Top with Cheese: Sprinkle the shredded cheddar cheese and grated Parmesan cheese evenly over the top layer of potatoes.
Bake: Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes. Then, remove the foil and continue baking for an additional 15 minutes, or until the potatoes are tender and the cheese is bubbly and golden brown.
Garnish and Serve: Once baked, remove the casserole from the oven and let it rest for a few minutes. Garnish with freshly chopped parsley if desired, and serve warm.