Combine all the ingredients into a highball glass, fill halfway with crushed ice, and swizzle for 10 seconds.
Top with more crushed ice.
Garnish with a mint sprig and lime zest.
*Eastern medicine syrup: Stir together 1 qt water, 1 qt sugar, 1 chopped 2-inch piece of fresh ginger, 2 makrut lime leaves, 1 tsp rosewater, 10 Korean chili threads, 6 cracked cardamom pods, 2 cracked lemongrass stalks and 10 mint leaves in a pot over medium heat, bring to a simmer, and steep for 1 hour. Chill the syrup, then strain through a cheesecloth or fine-mesh strainer, and store in the refrigerator. Makes 1 qt.