In a large skillet over medium heat, add a drizzle of olive oil. Once hot, add ground beef; cook for 6-8 minutes until browned. Stir in sliced mushrooms, cooking for an additional 4-5 minutes.

Reduce heat to low and sprinkle shredded cheese over the beef and mushroom mixture. Stir gently as cheese melts for about 2-3 minutes.

In a mixing bowl, combine Greek yogurt, grated cucumber, minced garlic, and chopped fresh herbs. Stir until smooth and refrigerate for 10 minutes.

Warm pita breads for about 30 seconds until soft. Open each pita and spoon in cheesy beef and mushroom mixture.

Drizzle tzatziki sauce over the filled pita pockets and serve immediately.