Mix yogurt, salt, garlic, lemon juice, and cucumber together in a small bowl. Chill in refrigerator until ready to eat.
Meanwhile, add ground beef, garlic, oregano, salt, and pepper to a skillet or shallow dutch oven. If you are using lean grass-fed beef, there won't be any fat to drain.
Evenly distribute spices throughout beef and cook beef over medium heat until brown and cooked through.
Serve spiced beef on flat bread with a generous helping of yogurt sauce and other desired toppings.
Possible toppings: lettuce, tomatoes, sliced onion, feta cheese