Preheat the oven to 375°F (190°C) and grease a 9x13-inch baking dish.

Heat olive oil in a large skillet over medium heat. Add ground beef and cook until brown, about 5-7 minutes.

Stir in chopped onion and minced garlic, cooking for an additional 3-4 minutes until softened.

Spread the beef mixture in the greased baking dish, then layer thinly sliced potatoes on top, seasoning with salt, pepper, Italian seasoning, and paprika.

Sprinkle shredded cheddar and grated parmesan cheese over the potatoes, then pour beef broth around the edges and drizzle milk on top if using.

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

Remove the foil and bake uncovered for 15-20 minutes, until potatoes are tender and cheese is golden brown.

Garnish with fresh parsley before serving hot.