In a bowl, combine cucumbers, tomatoes, and red onion. Add lemon juice, oregano, salt, and pepper. Toss well and set aside.
In a separate bowl, season the ground beef with cumin, oregano, salt, and pepper. Mix gently until just combined. If time allows, refrigerate for 20–30 minutes for better flavor.
Divide the beef into 4 equal portions and form into loose balls.
Preheat a griddle or flat-top to medium-high heat.
Place each beef ball onto the hot griddle. Immediately place a pita over each one and press down firmly with a spatula or burger press to flatten.
Cook for 2–3 minutes, until a crust forms on the beef and the pita begins to toast.
Flip and cook for another 1–2 minutes, until the beef is fully cooked (160°F internal temperature).
Remove from the griddle and top each with the cucumber tomato salad, a generous spoonful of tzatziki, and crumbled feta.
