Make the tzatziki first. Grate the cucumber, then squeeze out as much liquid as possible using a paper towel or cheesecloth.

In a small bowl, whisk together the Greek yogurt, drained cucumber, lemon juice, dill, grated garlic, and a pinch of salt. Refrigerate while you cook the beef.

Heat a large skillet over medium-high heat. Add a splash of olive oil if needed, then sauté half of the diced red onion for about 3 minutes until softened.

Add the minced garlic and cook for 30 seconds until fragrant, being careful not to burn it.

Increase the heat to high. Add the ground beef, break it apart slightly, then let it sit undisturbed for 60 to 90 seconds so a browned crust forms.

Continue breaking up and cooking the beef until no longer pink.

Push the beef to one side of the skillet. Add the tomato paste to the center and cook for 30 seconds to deepen its flavor.

Stir the tomato paste into the beef, then add oregano, cumin, thyme, cinnamon, salt, and black pepper.

Pour in the beef broth or water and simmer for 2 minutes until the liquid reduces into a glossy coating on the meat.

Warm the pitas in a dry skillet for 30 seconds per side, or wrap in foil and heat in a 350°F oven for 5 minutes.

Spread tzatziki over each warm pita. Top with spiced beef, sliced tomatoes, reserved raw red onion, olives, feta, and parsley.

Fold and serve immediately.