Bring 4 cups water to a boil with 1 cup each blueberries and fresh basil and 5 tablespoons sugar; stir to dissolve the sugar. Let cool 5 minutes. Add 12 white tea bags and steep 5 minutes. Strain through a fine-mesh sieve into a pitcher, gently pressing on the solids. Stir in 3 cups cold water. Chill. Serve over ice with blueberries and basil sprigs.