In a 1-gallon punch bowl, muddle the lemon peels with the sugar and let stand for 3 or 4 hours.
Add the lemon juice and stir until the sugar dissolves.
Add the remaining ingredients and stir to combine.
Slide in a 1-quart block of ice and garnish with freshly grated nutmeg.
Ladle into punch cups in 3-ounce portions.
(This recipe makes about 30 servings).