Combine all ingredients in a shaker filled with ice and shake well.
Strain into a rocks glass over ice. Garnish with a lime wheel or wedge and serve.
For the nut syrup (aka orgeat):
Toast the nuts in a small, dry saucepan over low heat until fragrant (agitate the nuts occasionally so that you toast all sides). Let cool and pulverize with a blender or food processor.
Add the pulverized nuts, sugar, and 1 cup water to the same saucepan and heat until almost boiling, stirring to dissolve the sugar. Remove from the heat and allow to steep for 3 to 12 hours. Strain through a cheesecloth or fine mesh strainer. (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.