Place cubed watermelon in a small bowl and puree with immersion blender (you could also use a regular blender or food processor for this.) Once pureed, strain fresh watermelon juice through a sieve into a cocktail shaker filled halfway with ice. Add remaining ingredients and shake vigorously for 20-30 seconds.

Fill two highball glasses about ¾ of the way with ice. Strain mixture in cocktail shaker into glasses, dividing evenly. Top with club soda and garnish with a watermelon cube and more fresh basil if desired.