Trim. Begin by preparing your chicken drumsticks. Using sharp kitchen shears. cut the skin and connective tissue off of the bone. Press the remaining leg meat on the drumsticks down so about 3 inches of the bone are exposed and the meat is somewhat condensed into a rounded "lollipop" shape.
Marinate. Place all of your trimmed lollipops into a large gallon zip-top bag and pour in 1 cup of the salad dressing. Seal the bag and gently toss to coat all of the drumsticks. Place in the refrigerator and allow to marinate for 6-8 hours.
Preheat. When you're ready to cook, start up your grill on medium heat. You want your temperature to be around 350 degrees F.
Season. Remove your chicken lollipops from the bag and discard the marinade. Season the chicken liberally with Beer Rub or equal parts salt and pepper. Place the drumsticks directly on the grill grates, close the lid, and cook for 30-35 minutes, turning every 10 minutes.
Make the glaze. While your chicken cooks, prepare your glaze. Combine the garlic salad dressing, Everything BBQ sauce, and honey in a small saucepan. Cook over medium heat, stirring often until the ingredients are well combined and the sauce starts to thicken (about 10 minutes). Transfer to a large bowl and allow to cool for a few minutes.
Sauce and finish cooking. Remove your chicken lollipops from the grill and place them in the bowl of sauce. Toss to thoroughly coat all of the chicken in the glaze. Return the lollipops to the grill and reduce the temperature to low. Cook for an additional 10 minutes or until the internal temperature reaches 165 degrees. F.
Enjoy. Transfer your chicken to a serving platter and serve with additional honey on the side, if desired.