Heat the oven to 375°F / 190°C. Coat a 9×13-inch baking dish with cooking spray or olive oil.

Warm the olive oil in a large skillet over medium heat. Add the ground beef and cook for 5–7 minutes, breaking it into smaller pieces as it cooks. Drain excess fat if necessary.

Stir the onion and garlic into the browned beef. Cook for 3–4 minutes, until the onion becomes soft and translucent.

Transfer the beef mixture to the prepared baking dish and spread it into an even layer. Cover the beef with the thinly sliced potatoes, then season them with salt, pepper, dried Italian seasoning, and paprika.

Distribute the cheddar and Parmesan evenly over the potatoes and beef. Pour the beef broth or water around the edges of the dish, then drizzle the optional milk over the top.

Cover the dish tightly with aluminum foil and bake at 375°F / 190°C for 30 minutes.

Remove the foil and bake for another 15–20 minutes, until the potatoes are tender and the cheese is bubbly and golden.

Sprinkle with fresh parsley if desired and serve the casserole hot.