Prepare the rosemary honey simple syrup. In a medium sauce pan, combine the honey, water and rosemary. Bring to just a boil over medium heat. Remove from the heat and let the rosemary steep for 10 to 15 minutes until fragrant. Once cooled, strain into a container.
In a martini shaker, add the gin, lemon, and 2 ounces of the rosemary honey simple syrup. Fill with ice and shake vigorously for 10 to 15 seconds to develop the honey "foam" that will settle on top. Strain into a martini or coupe glass. Top with a rosemary sprig for garnish.
If serving this for a party or event, prepare the rosemary honey simple syrup in advance and store in the fridge. Leave out at room temperature for about 30 minutes before using.
There is a decent amount of booze in each cocktail, we recommend serving it in a martini or coupe or some glass that implies it's a cocktail for sipping.