Step 1: Three hours before your party, peel 3 lemons with a swivel-bladed vegetable peeler, trying to end up with three long spirals of peel. Put them in a 3- or 4-quart fireproof bowl with ¾ cup demerara sugar or other raw sugar. Muddle the peels and the sugar together and let sit.
Step 2: Also before your party, squeeze enough lemons to make ¾ cup strained juice. Put this in a cup and refrigerate it. Measure into one container 1 cup VSOP-grade cognac and in another container combine 1 ¼ cups mellow amber rum, such as Mount Gay Eclipse or Angostura 1919, and 1 ¼ cups funky, strong Jamaican rum, such as Smith & Cross.
Step 3: Set 1 quart water to boil and put the bowl containing the lemon peels and sugar on a wooden cutting board or other heat-resistant surface in a spot where everyone can gather around. When the water boils, turn it off, gather your guests around the bowl, and pour in the cognac and rum, noting what you're adding and why.
Step 4: With a long-handled barspoon, remove a spoonful of the rum-cognac mixture and set it on fire. Return it to the bowl, using it to ignite the rest. Stir with a ladle or long-handled spoon, attempting to dissolve the sugar. Let burn for 2 or 3 minutes, occasionally lifting one of the lemon peels up so people can admire the flames running down it.
Step 5: Extinguish the flames by covering the bowl with a tray, and add the reserved lemon juice and the boiling water. (For cold punch, add 3 cups cold water, stir, and slide in a 1-quart block of ice, easily made by freezing a quart bowl of water for 24 hours.)
Step 6: Grate fresh nutmeg over the top and ladle out in 3-oz servings.
