Bring sugar, water, rosemary, and lemon zest to a boil in a small saucepan, stirring until sugar dissolves. Cover and remove from heat; let stand for 20 minutes. Strain, discarding solids, and refrigerate syrup.
Combine chilled syrup, lemon juice, and vodka. Pour over ice in a martini shaker. Shake until really cold. Strain into martini glass or old-fashioned glass, and garnish with small sprig of rosemary or a lemon twist, if desired.
This one takes a little prep time, but it’s worth it. Also, I like to mix 3 teaspoons of the lemon rosemary syrup into club soda for a non-alcoholic beverage. The syrup makes more than you'll need for 1 martini.
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