In a small food processor, pulse the chopped onion, garlic, and parsley until fine.
In a large mixing bowl, combine the onion mixture with ground beef, tomato paste, and spices. Mix until well combined.
Cut the pita breads in half or 1/4th and gently open them up. Stuff about 1/4 cup of the beef mixture into each pita pocket, pressing to evenly distribute, until about 1 inch thick. Optionally, add a layer of shredded cheese.
Stove-top Method: Heat a grill pan over medium-high heat. Brush both sides of the stuffed pitas with olive oil and grill for 2-3 minutes per side.
Oven Method: Preheat oven to 400F. Brush pitas with olive oil and bake on a lined sheet for 12-15 minutes, or air fry at 400℉ for the same duration, flipping halfway through.

Serve with shawarma sauce and garnish with fresh red onions and lemon slices.