In a large skillet over medium heat, cook the ground beef until browned, about 5-7 minutes. Drain excess fat if necessary.
Add the diced onion and sliced mushrooms to the skillet and cook until the vegetables are softened, about 5 minutes.
Stir in the minced garlic, oregano, salt, and black pepper. Cook for an additional 2 minutes until fragrant.
Remove the skillet from heat and stir in the shredded mozzarella cheese until melted and well combined.
While the beef mixture cools slightly, prepare the tzatziki sauce. In a bowl, combine the Greek yogurt, grated cucumber, lemon juice, dill, and garlic powder. Mix well and refrigerate for at least 10 minutes to allow flavors to meld.
To assemble, gently open each pita pocket and fill with the cheesy beef and mushroom mixture.
Drizzle with tzatziki sauce and serve immediately.
Notes
For added flavor, try mixing in some chopped spinach or bell peppers into the beef mixture.
To make it a complete meal, serve with a side of roasted vegetables or a simple green salad.