Stir together sugar, water and rosemary in a medium saucepan over medium-high heat. Bring to a boil, stirring occasionally, and boil 1 minute or until sugar is dissolved. Remove from heat, and let stand 1 hour.
Pour liquid through a wire-mesh strainer into a jar or airtight container, discarding rosemary sprigs. Cover and chill 3 hours.
Once syrup has chilled, add 1 oz of rosemary simple syrup and the other ingredients
to a cocktail shaker full of ice. Shake and strain into a chilled martini glass. Garnish with a sprig of rosemary.