Freeze watermelon on a parchment-lined baking sheet until firm.
Combine frozen watermelon, lime juice, basil and 2 tbsp sugar in a blender. Taste; add more sugar, if needed. Strain through a fine-meshed sieve into a large measuring cup or bowl (ideally with a spout). Discard the solids in the sieve. You should have 4 cups of watermelon juice.
Measure 1/2 cup watermelon juice into 8 tall, ice-filled glasses. Add 1 1/2 ounces vodka to each, then top up with ginger ale (approximately 1/2 cup ginger ale per serving).