Cut tempeh into 12 slices. Thinly slice onion, bell pepper and mushrooms.
In a large skillet heat 1 tablespoon of the sesame oil over medium heat. Add sliced tempeh and cook each side for 3 to 4 minutes until browned. Add balsamic vinegar and cook one minute; flip and cook an additional minute. Remove tempeh from skillet.
Add remaining sesame oil to skillet and heat over medium heat. Add the onion, bell pepper and mushrooms and cook until tender.
Cut pita in half and open to form a pocket. Spread each half with 1 teaspoon mayonnaise. Add 3 pieces tempeh and 1/4 the vegetable mixture to each pita half. Serve immediately.