How to Make It
In a large bowl, stir together the molasses, olive oil, port, mustard, soy sauce, pepper, Worcestershire sauce and shallot. Let stand at room temperature for 30 minutes. Add the chicken quarters and turn to coat. Refrigerate overnight.
Light a grill or preheat the broiler. Remove the chicken from the marinade and arrange the pieces on large rimmed baking sheets. Brush the chicken quarters with the Sweet Mustard Barbecue Sauce and grill over a medium-hot fire or broil 12 inches from the heat, turning often and rotating to cook evenly, until cooked through and nicely glazed, 8 to 10 minutes per side. Serve hot or at room temperature.