Start by reducing the blackberries in a small saucepan. Add blackberries and water and heat until it comes to a boil. While cooking carefully press blackberry with a fork to help break them down. Lower heat and continue to stir them and press them.
Strain the blackberries using a fine mesh strainer and reserve the juice. Make sure to press the blackberries to get more out of them.
Put the juice back in a saucepan and reduce until the juice thickens.
Put 2 tbsp syrup, basil, white wine vinegar, olive oil, and a pinch of salt into a jar and shake.