Add all ingredients to a shaker and dry shake for 15-20 seconds. Add ice and shake again until well-chilled.
Strain into a chilled coupe glass.
Garnish with a sprig of fresh rosemary.
Combine sugar, water, and rosemary sprigs in a small saucepan over medium heat. Bring to a simmer, stirring occasionally, until sugar is dissolved. Remove from heat and let sit at room temperature until completely cool.
Remove rosemary sprigs and store syrup in an airtight container in the fridge for up to three weeks.