Hull 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. Mash the basil once or twice to release the oils. Cover the bowl and refrigerate for 24-48 hours.
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 press it with a spatula to remove as much of the juice as possible. You should have about 3/4 cup of syrup.
Discard the fruit and basil, or use it to top ice cream or yogurt if you like.
Add the vinegar 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 2 tablespoons of the shrub syrup (or to taste) and stir. If desired, add alcohol.
Notes
Store syrup in a mason jar in the refrigerator. It should last at least three months if you don't open it frequently. This recipe makes approximately 1 1/2 cups. The nutrition info is for one serving or 2 tablespoons.