Berry caviar pearls
In a beaker or large measuring cup, combine 200 ml of water, the sodium alginate and the berry syrup. Mix with an immersion blender until the liquid is very smooth. Let rest for 30 minutes.
Meanwhile, dissolve the calcium lactate in 500 ml of water. Draw the treated berry syrup into a pipette or syringe and carefully dispense it, drop by drop, into the calcium lactate bath. After a few seconds, scoop out the pearls using a slotted spoon or small sieve, and rinse them in cool water.
Put the egg whites, simple syrup, vanilla bean and 150 ml of water into a whipping siphon. Screw on the head, add a gas cartridge and shake well.
Assembling the cocktail
Thoroughly shake together the vodka, Chambord liqueur and lime juice in a cocktail shaker. In a cold cocktail glass, add enough berry caviar pearls until it is 1/3 full. Strain the contents of the shaker into the glass, and top with some vanilla mousse. Garnish the mousse with berries of your choice.