Preheat oven to 375°F (190°C). Grease a 9×13-inch baking dish with a little oil or nonstick spray.

Heat olive oil in a skillet over medium heat. Add ground beef and cook, breaking it up until browned. Season lightly with salt and pepper.

Drain excess fat from the pan. Return the pan to the heat and add the chopped onion. Cook until soft and translucent, about 4–5 minutes. Stir in minced garlic and cook for another 30 seconds until fragrant.

Spread the beef-onion mixture evenly across the bottom of the prepared baking dish.

Arrange a single layer of thinly sliced potatoes over the beef. Sprinkle with a bit of salt, pepper, Italian seasoning, and paprika. Repeat with remaining potato slices until the top is covered.

Evenly sprinkle the shredded cheddar and grated Parmesan over the potatoes.

Pour beef broth or water around the edges of the dish. If using, drizzle the milk lightly over the top for extra creaminess.

Cover the dish tightly with foil and bake for 30 minutes.

Remove the foil and bake uncovered for an additional 15–20 minutes, until the potatoes are tender and the cheese is bubbly and browned.

Let the casserole rest for 5 minutes before garnishing with chopped parsley and serving hot.