Prepare the rim: Place granulated sugar in a single layer on a plate. Cut a notch in a lime wedge and run it around the rum of the glass to wet it. Then roll the rim in the sugar until evenly coated.
Shake the drink: Place the mango puree, vodka, Cointreau, lime juice, and simple syrup in a cocktail shaker. Add a handful of ice and shake until cold. Strain the drink into the prepared martini glass.
Notes
*To convert to tablespoons, 1 ounce = 2 tablespoons