Put the ice cubes, gin, lemon juice, cane sugar syrup and champagne into the blender. Blend for 15 seconds on speed 1.
Pour the cocktail into a glass filled with ice cubes.
Peel the lime zest with as little white pith as possible. Put the lime zest into the mini-chopper and process for about 3 pulses on speed 2, then arrange the pieces on the cocktail.