Stem the strawberries, and cut them into quarters.
Place the strawberries and sugar into a bowl that has a lid. Mash or muddle the berries and sugar until the berries are mostly broken apart.
Add the basil leaves to the bowl with the berries and sugar. Cover the bowl and refrigerate overnight.
Stir the berries to dissolve as much sugar as possible. Strain the liquid and any undissolved sugar into a measuring cup. Put the fruit and basil into a sieve or fine mesh strainer and remove as much of the juice as possible into the measuring cup. You should have about 1 cup of syrup.
Discard the fruit and basil, or use it to top ice cream or yogurt if you like.
Add the vinegars to the strawberry-basil syrup and stir well to combine. Pour the mixture into a jar or bottle with a lid, and refrigerate for at least a week.
To serve, fill a glass with ice and sparkling water. Add about 1 tablespoon of the shrub syrup and stir. If desired add alcohol.