The Green Vesper

Bring sugar and 1/2 cup water to a boil in a medium saucepan over medium-high heat. Reduce heat to medium-low, bring mixture to a simmer, and cook, stirring constantly, until sugar dissolves. Let cool slightly, pour into a heatproof vessel, and chill at least 35 minutes. Purée simple syrup and arugula in a blender until liquefied. Using a fine-mesh sieve or cheesecloth-lined colander, strain mixture into an airtight container and chill.