Heat the water to 75–80°C (167–176°F), do not boil. Add the white tea bags and steep for 3–4 minutes. Remove the tea bags and let the tea cool to lukewarm. This tea is intentionally stronger than normal.
Add the blueberries and basil leaves to a blender. Blend briefly just until smooth and aromatic. Do not overblend or heat the mixture — the basil should stay green and fresh.
Strain the mixture through a fine-mesh sieve into a bowl or measuring jug. Do not press the pulp. Discard the solids and keep the smooth, deeply colored liquid.
Stir 200–240 ml of the strained basil blueberry liquid into the cooled white tea. Taste. The base should be softly fruity and clearly herbal, not sweet or thick.
Refrigerate the base for 1–2 hours until fully cold.
Just before serving, gently stir in the ice-cold club soda. Mix slowly to preserve carbonation.
Fill glasses with ice, pour over the sparkling basil blueberry cooler, and garnish with fresh blueberries and basil leaves.