Place blackberries, basil, and rice malt syrup in a large jar. Mash to a pulp with a muddler (or the end of a wooden spoon), then stir in the vinegar and balsamic dressing. Cover and put in the fridge for 24-48 hours to allow the flavours to develop.
Remove from the fridge and strain using a large tea strainer, pressing on the solids to extract all the flavours. Keep the pulp for using in your smoothies.
Pour the shrub into a jar or bottle with a lid, and store in the fridge. It should keep for at least a month.
To serve, add about a tablespoon of shrub to your glass and pour over with sparkling water.