Preheat the oven to 375°F (190°C) and thinly slice the potatoes to about ¼-inch thick. Grease a baking dish with olive oil.

In a large skillet, heat olive oil over medium heat. Add diced onions and minced garlic, sautéing for 3-4 minutes until fragrant. Crumble in the ground beef and season with Italian seasoning, paprika, salt, and pepper. Cook until browned, about 5-7 minutes, then remove from heat.

Layer half of the sliced potatoes at the bottom of the greased baking dish, followed by half of the cooked beef mixture, spread evenly. Sprinkle half of the shredded cheddar cheese over the beef. Repeat the layering process with remaining ingredients.

Pour beef broth over the layers in the baking dish, mixing in the milk for extra creaminess if desired. Ensure even distribution of the liquid.

Cover with aluminum foil and bake for 35-40 minutes. Remove foil, sprinkle Parmesan cheese on top, and bake uncovered for an additional 10 minutes until golden.

Let rest for 5 minutes before serving. Garnish with freshly chopped parsley and enjoy!