To make the shrub: In a small pan on medium-low heat, combine all of the ingredients except for the vodka. Cook, stirring, for 10 minutes. Strain the shrub into a heat-safe glass jar (like a mason jar), and let the mixture cool to room temperature.
Fill a tall glass with ice, and add 1/4 cup of the shrub, and 1 ounce vodka. Top the glass off with the seltzer, give it a good stir, and serve with a fresh sprig of rosemary.