Combine the cold water and the cornstarch in a small skillet and using a fork or your fingers stir the cornstarch to remove any lumps. Heat the water-cornstarch mixture over medium heat, stirring constantly until it becomes thick and pasty. Reduce the heat to very low and cook this mix mixture for 5 minutes, while stirring with a wooden spoon or heat resistant spatula. Pour it onto a plate and refrigerate until thoroughly chilled.
Place the chilled, and solidified cornstarch base into a blender along with the olive oil, vinegar, basil, garlic, salt and pepper. Blend the vinaigrette on high for a minute or two, or until it is very smooth and thoroughly emulsified. The vinaigrette will keep for about 1 week under refrigeration. If it separates between uses return it to the blender for a few seconds.
