Place almonds, pine nuts, garlic, grapes, grape juice, water, and bread in a blender and puree until smooth. Strain the mixture into a bowl. Chill the soup for at least 30 minutes.
Remove soup from refrigerator and fold the whipped heavy cream into the soup. Finish with a few tablespoons each of the verjus and walnut oil. Ladle into serving bowls and garnish each with chives, almonds and grapes, if desired.