Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and spread the coals evenly over entire surface of coal grate. Set cooking grate in place, cover gill and allow to preheat for 5 minutes. Clean and oil the grilling grate. Add brown sugar, rum, butter, and vanilla to a small saucepan and place on the grill. Cook until butter is melted and sugar is dissolved. Remove from heat.