A few hours before preparing the punch, peel 4 lemons with a vegetable peeler or paring knife to create 4 long spirals of peel.
Put them in a heatproof bowl with ¾ of a cup of demerara sugar.
Muddle the peels and the sugar together and let sit at room temperature.
Juice the 4 peeled lemons (and any extra needed) through a strainer to yield 6 oz. of strained juice. Set aside in the fridge.
Measure the rum and Cognac into a pitcher or other pouring vessel.
To prepare the punch, boil the water and place the bowl containing the lemon peels and sugar on a wooden cutting board or other heat-resistant surface in an open area.
Pour the Cognac and rum into the bowl.
Use a long-handled barspoon to remove a spoonful of the rum-cognac mixture.
Light the spoonful on fire with a match and hold it just above the surface of the bowl in order to ignite the rest of the liquid.
Stir with the barspoon or a heatproof ladle to help dissolve the sugar.
Let the mixture burn for 2 or 3 minutes, occasionally lifting out one of the lemon peels with the ladle or spoon to show the flames running down it.
Cover the bowl with a large heatproof dish or tray to extinguish the flames.
Add the lemon juice and the hot water.
(For cold punch, replace the hot water with 3 cups of cold water and add a 1-quart block of ice, made by freezing a quart bowl of water for 24 hours.)
Stir.
Grate fresh nutmeg over the top and ladle out in 3-ounce servings.
