For the Broccoli Slaw in this stellar BBQ Chicken Sandwich recipe we use plain Greek yogurt, which is a wonderful low-fat substitute for mayonnaise. It has the right texture, and when mixed with other... flavors as here, you can get guys who would otherwise turn their noses up at yogurt to happily chow down on it. The probiotics in the yogurt will do you all so much good! Give it a try at your next cookout.
In a medium saucepan, bring 4 quarts of water to a boil. Add chicken breasts. Reduce heat to simmer and cook until the chicken is fully cooked, about 15 minutes. Remove chicken from liquid and let cool. Once the chicken is cool, use 2 forks to shred the meat. Place into a large bowl. Set aside.
Meanwhile, in a small saucepan, combine ketchup, Worcestershire sauce, apple cider vinegar, and agave. Bring to a simmer and cook for 10 minutes. Pour the sauce into the bowl with the chicken and coat the chicken with the barbeque sauce.
In a separate medium bowl mix together the Greek yogurt and red wine vinegar. Season with salt and pepper to taste. Add the carrots, julienned broccoli and apples to the yogurt mixture. Mix to coat the sauce with the vegetables.
To assemble each sandwich, place a quarter of the chicken on the bottom on each bun. Next place a quarter of the broccoli slaw on top of the barbecue chicken. Place top of bun on top and serve.