Set up a blender and pour the blueberries into it. Puree them completely. Then add the rum, lemon juice and sugar. Blend that all together more by pulsing it a few times. Finally, add the basil and pulse the blender twice to incorporate it. Get out two tall cocktail glasses and fill them with a little ice. Pour half of the blueberry mixture into each of them, then fill the glasses the rest of the way with the club soda. Garnish with additional blueberries and basil on top and serve immediately!