Preheat the oven to 375°F (190°C). Grease a 9×13-inch baking dish.

Heat the olive oil in a skillet over medium-high heat. Add the ground beef and brown it, breaking it up with a spoon. Season with salt and pepper.

Drain excess fat from the pan, leaving a little for flavor. Stir in the chopped onion and minced garlic. Sauté until the onion is soft and translucent, about 4 to 5 minutes.

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

Arrange a single layer of thin potato slices over the beef. Sprinkle with a pinch of salt, a little paprika, and a dusting of Italian seasoning. Repeat layers until potatoes are used.

Pour the beef broth or water around the edges of the dish. If you want a creamier texture, drizzle the milk over the top before adding cheese.

Sprinkle the shredded cheddar and grated Parmesan evenly over the potatoes. Cover the dish tightly with foil.

Bake covered for 30 minutes. Remove the foil and bake for another 15 to 20 minutes, or until the potatoes are tender when pierced with a knife and the cheese is golden and bubbling.

Let the casserole rest for about 5 minutes before cutting. Garnish with chopped fresh parsley if you like, then serve.