Heat a tablespoon of olive oil in a skillet over medium heat. Sauté minced garlic for about 30 seconds until fragrant. Add lean ground beef, dried oregano, ground cumin, salt, and pepper; brown for 7-8 minutes.

While the meat is cooking, whisk together plain Greek yogurt, finely grated garlic, fresh lemon juice, a drizzle of olive oil, and a pinch of salt in a bowl until smooth and creamy.

Lightly warm the pita bread or flatbreads in the skillet for about 1-2 minutes on each side or wrap them in a damp paper towel and microwave for about 30 seconds.

Spread garlic yogurt sauce over each warm pita. Add a hearty portion of beef mixture followed by cucumbers, tomatoes, and red onions. Sprinkle feta on top and add parsley or dill.

Fold or roll each wrap tightly and serve immediately while warm.