Preheat oven to 400 degrees F. In a medium nonstick skillet, cook ground beef, onion, and garlic until meat is browned; drain off fat. Stir tomato sauce and rosemary into meat mixture in skillet. Bring to boiling; reduce heat. Simmer, uncovered, for 2 minutes.
Carefully split pita bread rounds in half horizontally; place pita halves, rough sides up, in a single layer on a large baking sheet. Bake for 3 to 4 minutes or until lightly toasted.
Top toasted pita bread with meat mixture; sprinkle with mozzarella cheese. Bake for 2 to 3 minutes more or until cheese is melted. Remove from oven. Top with spinach, tomato, feta cheese, and, if desired, olives; serve immediately.