Using a small, sharp knife or peeler, remove the peel from the orange in a long intact spiral, about 1-inch wide.  Remove the peel from the lemon in the same manner, but about 1/2  inch wide.  Reserve the fruit for another use.

Light the burner under a brûlot bowl or chafing dish and adjust the flame to low. Into the bowl place the orange and lemon peel, sugar, cloves, cinnamon sticks and orange liqueur. Heat for 1 to 2 minutes, stirring constantly with a long-handled ladle, to dissolve the sugar and warm the ingredients.  Using a fork, remove the orange peel and set aside leaving the prongs of the fork still attached.

When the mixture is warm, ignite with a match.  Pour in the hot coffee.

Quickly, while the mixture is still flaming, hold the spiraled orange peel with the prongs of a fork over the bowl, and ladle the flaming coffee mixture down the peel several times into the bowl for a spectacular presentation.

Ladle the café brûlot into brûlot, demi-tasse, or coffee cups, being careful to leave the flavorings (peels, cloves, cinnamon) in the bowl. Serve immediately while hot.

Note: The coffee is prepared in and served from a special decorative bowl positioned over a flame, and the finale consists of the flaming coffee being ladled down a long spiral of orange peel back into the bowl. A Brulot ladle is specially designed with a small strainer at the end so that the bits of peel, cloves and cinnamon do not get served to guests. The finished beverage is served in tall, thin, footed mugs, often decorated with a full-length portrait of the devil, reference to the drink's other name, "Cafe Diabolique" or "Devil's Coffee," perhaps so named for the punch it packs!