If you did decide to bring first, remove from liquid and pat dry with paper towels. Right out of package, rinse and pat dry skin. Place chicken quarters on a wire rack with a rimmed sheet pan or the casserole dish if it fits. Place in refrigerator 12-16 hours until the skin is dry.
Fill smoker with hardwood BBQ pellets. Prepare smoker by placing 2-3 long sheets of aluminum foil along the bottom of the smoker element, underneath the rack, for easy cleanup. Brush grill rack clean. Set smoker to smoke.
Once it starts smoking, set temperature to 250°. Place chicken quarters on smoker, skin side up. In a small bowl, mix together mustard sauce ingredients. Cover and set aside until ready to serve.
When chicken reaches internal temperature of 165°, after about 1.5 hours, then remove from smoker.
Allow to rest 3-5 minutes. Brush skin with mustard sauce and serve.