Remove about 2 ounces beer and poke 2 holes in top of can. Hold chicken upright (legs pointing down) and insert opened beer can into cavity. Stand chicken in upright position in center of grill. Position legs to best support chicken (similar to a tripod). Close lid. Grill 55 minutes or until chicken is cooked through. Remove chicken from can before serving
To prepare the sauce, melt the butter in a medium saucepan. Whisk in the brown sugar and heavy cream. Let the mixture just come to a boil. Let cool for a minute, then add the rum. The rum sauce can be made up to two days ahead of time. Reheat until just warm.
When ready to serve, cut the bread pudding into squares and place onto dessert plates or into small dessert bowls. Drizzle generously, the hot buttered rum sauce over the top.