Preparation Place brown sugar, butter, cinnamon, nutmeg, and cloves in food processor. Scrape in seeds from vanilla bean. Process until blended. DO AHEAD Butter mixture can be made 1 week ahead. Wrap in plastic and chill. Bring 4 cups water to boil in large saucepan. Add rum, brandy, and butter mixture; stir until butter melts. Ladle into mugs and garnish with cinnamon sticks.
Preparation Place brown sugar, butter, cinnamon, nutmeg, and cloves in food processor. Scrape in seeds from vanilla bean. Process until blended. DO AHEAD Butter mixture can be made 1 week ahead. Wrap in plastic and chill. Bring 4 cups water to boil in large saucepan. Add rum, brandy, and butter mixture; stir until butter melts. Ladle into mugs and garnish with cinnamon sticks.