In a small skillet, melt butter over medium-low heat. Stir in the vanilla, spices and orange peel. Remove from the heat; add Cognac. Return pan to the heat and carefully ignite Cognac mixture.
Slowly pour brewed coffee over flames to extinguish. Discard orange peel; stir in brown sugar until blended. Ladle into mugs. Serve immediately with cinnamon sticks and whipped cream if desired.
Editor's Note: Keep liquor bottles and other flammables at a safe distance when preparing this beverage. We do not recommend using a nonstick skillet.
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