Light the burner under a brulot bowl or chafing dish and adjust the flame to low. Drop the orange and lemon peel, sugar cubes, cloves, and cinnamon stick into the bowl or pan, pour in the cognac and curacao, and stir to dissolve the sugar. When the mixture is warm, ignite it with a match. Stirring gently, pour the coffee into the bowl in a slow, thin stream; continue to stir until the flame dies out. Ladle into brulot cups or demitasse cups and serve at once.