Add blackberries, grapefruit, basil and honey to the blender and pulse to obtain a smoothie.
Use a fine mash sieve to remove the seeds, leaves and unwanted fruits chunks.
Add the fruit mixture, vodka and some ice cubes into a shaker and shake vigorously to chill.
Divide ice cubes into the serving glasses and evenly divide the vodka cocktail, then evenly pour soda.
Grind the peppercorns over the top and serve garnished with basil leaves.