Preheat the oven to 375 °F (190 °C).
In a skillet over medium heat, melt butter and sauté onion until soft, about 3–4 minutes. Add garlic and cook another minute.
Add ground beef, breaking it apart with a spoon. Season with paprika, oregano, salt, and pepper. Cook until the beef is no longer pink, about 6–8 minutes; drain excess fat if necessary.
In a bowl, whisk together milk and sour cream, and stir in half of the cheddar cheese.
In a greased baking dish, layer half of the sliced potatoes. Top with the cooked beef mixture, then cover with the remaining potato slices. Pour the milk‑cheese mixture evenly over the top.
Cover the dish with foil and bake for 35 minutes.
Remove the foil and sprinkle the remaining cheddar cheese over the top. Return to oven and bake uncovered for another 15–20 minutes, or until the potatoes are tender and cheese is bubbly and golden.
Let rest for 5 minutes before serving. Garnish with parsley.
