Heat a tablespoon of olive oil in a large skillet over medium heat. Add minced garlic and sauté for about 30 seconds until fragrant. Stir in ground beef, dried oregano, ground cumin, salt, and black pepper. Cook for 7–8 minutes, breaking it apart, until browned and cooked through.

In a small bowl, combine Greek yogurt, grated garlic, lemon juice, and a pinch of salt. Whisk together until smooth and creamy.

Warm pita or flatbreads in a dry skillet for about 30 seconds on each side. Spread garlic yogurt sauce across each wrap, layer with cooked beef, diced cucumber, chopped tomatoes, red onion, and feta cheese. Garnish with parsley or dill.

Fold or roll each wrap tightly, ensuring all fillings are inside. Serve warm and enjoy immediately.