To make the rosemary syrup, heat the water, sugar and chopped rosemary leaves in a small saucepan, stirring occasionally, until the mixture is hot and sugar is dissolved. Remove from heat and let cool completely. Once cool, strain the rosemary syrup into a jar, and refrigerate until ready to use.
To make the rosemary gimlet, measure the gin, lime juice and rosemary syrup into a cocktail shaker. Fill the shaker halfway with ice, and shake the cocktail mixture about thirty seconds. Pour into a cocktail glass. Garnish with a sprig of rosemary or a slice of fresh lime.
Recipe by Allons-Eat! at https://www.allonseat.com/rosemary-gimlet/