Preheat the oven to 375°F (190°C). Grease a 9x13-inch baking dish with a little oil or nonstick spray.

Heat the olive oil in a skillet over medium heat. Add the ground beef and cook, breaking it apart, until no pink remains, about 6–8 minutes. Drain excess fat if needed.

Add the chopped onion to the skillet and cook for 3–4 minutes, until softened. Stir in the minced garlic and cook for 30–60 seconds until fragrant. Season with salt and pepper. Remove from heat.

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

Arrange the thin potato slices in overlapping layers on top of the beef. Sprinkle the Italian seasoning, paprika, and a bit more salt and pepper over the potatoes.

Scatter the shredded cheddar and grated Parmesan over the potatoes in an even layer.

Pour the beef broth (and milk if using) around the edges of the dish so it seeps between layers but does not wash away the cheese.

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

Remove the foil and bake another 15–20 minutes until the cheese is golden and the potatoes are tender when pierced with a knife.

Let the casserole rest for 5 minutes before serving to settle the layers.