1. In a large nonstick frying pan, sauté onions in oil over low heat until soft, brown, and caramelized, at least 45 minutes to an hour. Add pastrami and sauté an additional five to 10 minutes. Add sauce ingredients and mix well to combine.
2. Divide mixture in two and set one half aside for topping, keeping it warm. Allow the other half to cool slightly.
3. Place ground beef into a medium-sized bowl and break up with a fork. Add salt and pepper and the cooled half of the onion-pastrami mixture. Mix well to combine.
4. Heat your grill to medium-high. Stuff the pita halves with the ground beef filling, packing it in well and dividing evenly among the eight halves. Lightly spray both sides of the pitas with cooking spray.
5. Place the pitas, meat side down (don’t worry, the filling won’t fall out!), directly onto your grill grates. Lower temperature slightly and grill for five to six minutes. Flip the pitas onto their sides and grill each side for an additional two to three minutes, being careful not to burn them. Don’t worry if they are slightly scorched; that makes them crispy!
6. Serve immediately with extra pastrami and onion sauce heaped over the top.