How to Make It
Use a large wooden spoon to crush basil leaves and stems with sugar in a medium bowl. Pour in lime juice and stir until sugar has dissolved.
Working in batches, puree watermelon cubes in a blender or food processor until smooth. Use a rubber spatula to press watermelon juice through a fine-mesh strainer into a pitcher. Discard watermelon pulp.
Pour reserved basil syrup through the same fine-mesh strainer into watermelon juice. Discard leaves and stems. Add vodka to juice mixture and stir to combine.
Fill 8 large glasses with ice, pour mixture over and serve immediately. Garnish with watermelon wedges and basil leaves, if desired.