Preparation

• In a medium saucepan, whisk the brown sugar, cumin, and cardamom pods with 1/2 cup water over medium heat until the sugar dissolves and the mixture is thick and syrupy, 5 to 6 minutes. Strain into a container through a fine-mesh strainer. Let cool, then refrigerate. (The syrup will keep, covered and refrigerated, for 2 months.)
• Put the mint leaves in a cocktail shaker. Using a muddler or a wooden spoon, press firmly on the leaves while turning the muddler to release the aromas. Add the rum, 1/2 cup of the spiced syrup, and the lime juice to the shaker. (Throw in a juiced lime half, too, if you like.) Fill with ice and shake until thoroughly chilled, about 15 seconds. Fill glasses with fresh ice and strain the drink into the glasses, leaving some room. Top off each glass with a splash of sparkling water. Garnish with lime wheels and mint leaves. Serve right away.