1. Make the Whole-Berry Cranberry Simple Syrup: Stir together sugar, cranberries, lime zest, and 2 tablespoons water in a small saucepan. Cook over medium-high, stirring constantly, until cranberries just start to burst, about 5 minutes. Remove from heat; let cool completely. Refrigerate, covered, until cold, at least 1 hour and up to 1 week.

2. Make the cocktail: Fill a 12-ounce glass with ice cubes. Stir in vodka, lime juice, ginger beer, and 3 tablespoons cranberries and syrup from Whole-Berry Cranberry Simple Syrup. Garnish with lime rounds.