Make the syrup: In a small saucepan, combine water and sugar then bring to a boil. Add in ginger and rosemary and return the mixture to a boil, stirring to fully dissolve sugar. Remove from heat then let the syrup cool completely (30-45 minutes). Strain the syrup through a fine mesh strainer into a jar or small bowl. Discard the solids then refrigerate until needed! Syrup can be refrigerated for up to one month in an airtight container.

Make the cocktail: In a cocktail shaker (or measuring cup), shake (or mix) together bourbon, rosemary ginger syrup and lemon juice. Fill two rocks glasses or mule mugs with lots of ice or one big ice cube (I love these huge square ice cubes). Place lemon slices in the glass between the ice and wall of the glass. Split contents of the shaker between the two glasses then top each cocktail with ginger beer plus a small rosemary sprig. Enjoy!