Juice the grapefruit to produce 2 oz of fresh juice.
In a shaker, add a sprig of rosemary, cane sugar, and the gin. Muddle until most of the sugar is dissolved and the rosemary becomes fragrant.
Add grapefruit juice and lemon juice. Shake for 30 seconds.
Pour mixture into a rocks glass with ice. Top with club soda.
Add a sprig of rosemary into the cocktail to garnish.