In a skillet, heat olive oil over medium heat until shimmering. Add minced garlic and sauté for about 30 seconds until fragrant. Mix in ground beef, oregano, cumin, salt, and pepper. Cook for 7-8 minutes until browned.

In a small bowl, whisk together Greek yogurt, grated garlic, lemon juice, and olive oil. Season with a pinch of salt and let it chill in the refrigerator for a few minutes.

Warm the pitas or flatbreads in a dry skillet for about 1 minute on each side until soft and just beginning to brown.

Set up an assembly line with warm pitas, garlic yogurt sauce, cooked beef, and fresh toppings. Spread yogurt sauce on each pita, add spiced beef, and top with vegetables and feta cheese.

Once assembled, fold or roll the pitas around the filling and serve immediately while warm.