1. Cut the cutlets, pastrami, peppers, and red onion into one- and- half-inch (four-centimeter) pieces.
2. In a medium bowl, whisk together all marinade ingredients. Reserve half of the sauce for basting. Place cutlets and half of the sauce in a ziplock bag and marinate in refrigerator at least three hours or overnight.
3. Thread chicken, pastrami, pineapple, peppers, onion, and cherries onto skewers. Avoid pit when you pierce the cherries. Spray assembled skewers lightly with cooking spray.
4. Preheat grill to medium heat. Place kabobs on grill, turning every three to four minutes, and basting with remaining marinade until chicken is done, about 10 minutes.
To broil kabobs in the oven, preheat broiler. Arrange kabobs in single layers on a baking sheet or broiler pan. Place under broiler. Turn kabobs every three to four minutes, basting with remaining marinade until chicken is done, about 10–15 minutes.