Combine all ingredients in a blender with ice and blend until slushy. Pour into a rocks glass. Garnish with a small pinch of ground nutmeg.
For the spiced syrup:
Toast whole cloves and allspice in a small, dry saucepan over low heat, agitating occasionally, until fragrant (just a few minutes).
Add the sugar and 1 cup water. Heat until almost boiling, stirring to dissolve the sugar. Remove from heat and add the lime peels. Cool completely and then strain. (The syrup will keep in the fridge for up to 2 weeks).
Irene runs a monthly Brooklyn-based pop-up series called Yooeating, with new takes on Korean home cooking, street food, and drinking culture by pairing with other culinary cuisines that feel like home.