Prepare the Potatoes
Preheat the oven to 375°F (190°C). Grease a 9x13-inch baking dish and set aside.
Peel and slice the potatoes into thin rounds, about 1/8-inch thick. Set aside.
Cook the Ground Beef
Heat the olive oil in a large skillet over medium heat. Add the chopped onion and minced garlic, cooking for about 3-4 minutes until softened.
Add the ground beef to the skillet, breaking it apart with a spoon. Cook until the beef is browned and cooked through, about 5-7 minutes. Drain any excess fat if necessary.
Season the Beef
Stir in the oregano, paprika, salt, and pepper. Mix well to evenly coat the beef with the seasonings. Add the beef broth and stir to combine. Let the mixture simmer for about 2-3 minutes to allow the flavors to meld together.
Assemble the Casserole
In the prepared baking dish, layer half of the sliced potatoes at the bottom. Spread half of the seasoned beef mixture over the potatoes, then repeat the layers with the remaining potatoes and beef.
In a small bowl, mix together the sour cream and milk (if using), then spread it evenly over the top of the casserole. This will help create a creamy texture as it bakes.
Top with Cheese
Sprinkle the shredded cheddar cheese evenly over the top of the casserole.
Bake the Casserole
Cover the baking dish with aluminum foil and bake in the preheated oven for 40-45 minutes. After 40-45 minutes, remove the foil and bake for an additional 10-15 minutes, or until the cheese is melted and bubbly, and the potatoes are tender.
Serve
Remove from the oven and let the casserole rest for 5-10 minutes before serving. Garnish with fresh parsley or green onions if desired.