The tangy barbecue sauce used in this recipe is inspired by the sauce served at Hamburger Mary's in Chicago. The slightly loose consistency and punch of flavors from the red wine vinegar and crushed red pepper pair extremely well with simply grilled chicken breasts.
Place the chicken breasts between 2 pieces of plastic wrap and pound lightly until they are of even thickness throughout.
Meanwhile, combine the vinegar, ketchup, brown sugar, soy sauce, and spices in a small bowl. Whisk in the tomato paste to thicken. Transfer the chicken to a sealed container and coat the breasts with half of the barbecue sauce, then marinate in the fridge for at least 2 hours.
When you're ready to grill, place a cast-iron grill pan over medium-high heat and cook the chicken for 5-6 minutes per side (or until cooked through). While the chicken is grilling, add the remaining sauce to a small saucepan over medium-low heat and cook until the chicken is done. Top the chicken breasts with the extra barbecue sauce before serving.