Heat oven to 375°F (190°C). Grease a 9×13-inch baking dish.
Peel and slice potatoes into even ¼-inch slices.
Melt butter in a large skillet over medium heat. Cook onion until soft, then add garlic.
Add ground beef and cook until browned. Season with salt, pepper, paprika, and oregano. Drain excess grease.
Sprinkle flour over the beef. Stir and cook for 1 minute.
Gradually stir in beef broth, milk, and cream of mushroom soup. Cook until the sauce becomes lightly thickened.
Layer half the potatoes in the baking dish, followed by half the beef mixture. Repeat.
Cover tightly with foil and bake for about 45 minutes, or until the potatoes are tender.
Remove foil and sprinkle cheese over the top.
Bake uncovered for 8–10 minutes, until the cheese melts and bubbles.
Rest for 10 minutes. Garnish with parsley and serve.