Pour sugar onto a saucer. Wet the rim of the glass with the lime wedge and dip into sugar to coat. Squeeze lime wedge into cocktail shaker filled with ice; add basil leaf and muddle. Pour in vodka, watermelon juice, and simple syrup; shake well to combine. Strain into cocktail glass and serve at once.

Note: ​Half of one large watermelon will yield approximately 2 quarts of watermelon juice. Seed it and purée in batches, straining through a fine mesh strainer.