To make the Rosemary Simple Syrup, add the water, sugar, and rosemary to a saucepan.
Cook over medium heat until the sugar dissolves, about 3-6 minutes.
Remove from heat and let the rosemary steep in the syrup for at least 10 minutes, up to 1 hour for deeper flavor. Strain the rosemary and pour it into a container. Let cool completely, about 1 hour.
Add the grapefruit juice, vodka, rosemary syrup, and lemon into a cocktail shaker with ice.
Shake and pour over ice into 2 glasses. Garnish with rosemary sprig and grapefruit slice.