Pour the purée carefully into the glass. Slowly add the sparkling wine, stirring as you do to combine the purée with the bubbly. Garnish with the blackberries on the toothpick or cocktail stick.
Make a simple syrup by combining the water and sugar in a small saucepan. Bring the mixture to a boil until the sugar has dissolved completely. Set aside to cool.
In a blender, purée the blackberries, lemon juice and the simple syrup together. Strain the mixture through a fine-mesh strainer to remove any seeds and to ensure the purée is smooth.
Alternatively, if you don't have a blender, place the blackberries, lemon juice, sugar and 2 tablespoons of water in a nonreactive saucepan. Heat slowly until the sugar has dissolved. Simmer until the blackberries have broken up in the pan. Then strain through a fine mesh strainer.
Once made, store in the refrigerator and use within a couple of days. This recipe makes about 5 servings.