For the shrub syrup (makes about 1½ cups syrup)
Mix strawberries and sugar in a nonreactive bowl, mashing strawberries to blend with sugar. Store in refrigerator for 24–36 hours, until there is a substantial amount of juice. Add vinegar and return to refrigerator for about a week. Strain liquid into a glass jar and store in refrigerator.
For the soda (makes 1 drink)
Pour shrub syrup into a tall glass. Add basil, lightly crushed. Muddle the basil in the syrup to blend flavors. Add ice, and top off glass with club soda. Stir well, and add optional basil sprig for garnish (adjust ratios of shrub and soda to your own taste).