For the syrup: Add the honey to the hot water and stir to dissolve. Chill before using.
For the mojito: Muddle the arugula, lime juice and 3/4 ounce honey syrup together. Add the gin. Shake and strain over ice. Serve in a rocks glass.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.