Make the Filling:
Heat olive oil in a skillet over medium heat. Add onion and garlic, sauté until softened (2–3 minutes).
Add ground beef and cook until browned, breaking it up with a spoon (5–6 minutes). Drain excess fat if needed.
Stir in mushrooms and cook until soft and liquid evaporates (3–4 minutes).
Season with smoked paprika, cumin, salt, and pepper. Mix and set aside.

Prepare the Tzatziki:
Grate the cucumber and squeeze out extra moisture using a towel.
In a bowl, mix the Greek yogurt, cucumber, garlic, lemon juice, dill, and salt. Chill until serving.

Assemble the Pitas:
Warm pita pockets in a skillet or microwave until pliable.
Stuff each with the beef mixture, sprinkle cheese inside.
To melt cheese, heat in a skillet or under the broiler for 1–2 minutes.

Serve:
Drizzle or spoon tzatziki sauce into each pita. Garnish with fresh herbs if desired.