Prepare the Tzatziki Sauce: In a small bowl, combine the Greek yogurt, grated cucumber, minced garlic, fresh dill, and lemon juice. Stir well until all ingredients are mixed. Season with salt and pepper to taste. Refrigerate while you prepare the rest of the meal to allow the flavors to meld.
Season and Cook the Meat: In a medium bowl, combine the ground lamb or beef with oregano, cumin, rosemary, garlic powder, salt, and pepper. Mix well to ensure the spices are evenly distributed.
Sear the Meat: Heat the olive oil in a large skillet or griddle over medium-high heat. Add the seasoned meat to the pan and cook for 5-7 minutes, breaking it up with a spoon, until it is cooked through and browned. For a more authentic texture, you can thinly slice a piece of lamb or beef and pan-sear it.
Assemble the Gyro: Warm the pita breads in a dry skillet for 30 seconds per side, or microwave them briefly.
Build the Gyro: To assemble each Greek gyro sandwich, place a spoonful of the cooked meat in the center of a warm pita. Top with a generous amount of tzatziki sauce, followed by slices of red onion and chopped tomatoes. Fold the pita around the filling and serve immediately.
Notes
This recipe can also be made with pre-made sliced gyro meat for an even quicker meal.