Build the base: Place the freeze-dried blackberries into a large pitcher. Don't crush them—let them stay whole.
Pour the juice: Pour the chilled blackberry juice into the pitcher until it reaches about three-quarters full. Watch the color as it pours.
Add the coconut milk: Slowly pour the well-stirred coconut milk over the blackberry juice in a thin stream against the side of the pitcher, creating a billowing cloud effect.
Stir gently: Stir gently one or two times to enhance the marble effect without fully blending the layers. Two gentle turns is the maximum.
Fill and serve: If using ice, fill serving glasses with cubes. Pour the prepared drink over the ice. Top each glass with remaining freeze-dried blackberries. Serve immediately.
Notes
Chill everything including glasses. Stir coconut milk well before measuring. Don't over-stir. Serve within ten minutes for best appearance.