Warm a heatproof bowl or mug.
Add the cognac, orange curaçao, cinnamon stick, star anise and a long spiral of orange peel.
Warm the mixture gently — do not boil it — then carefully ignite the surface with a long match, standing well back.
Let it burn for 20 seconds, ladling the flaming liquid over the spiral to caramelise the oils.
Extinguish it by pouring in the hot coffee, stir once, and strain into warmed cups.
A Creole tradition associated with Antoine's in New Orleans, where it has been served tableside since the 19th century. The flame is not decoration — it burns off harshness and caramelises the citrus oils. Warm the spirit first; cold brandy will not light, and chasing it with a match is how people burn their hands.
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