Cut the melon into slices. Remove the flesh from the skin and cut into bite-sized pieces on the skin. Divide into 4 plates. Put eggs, sugar, sparkling wine, cornstarch, lemon juice and zest in a high pot and mix with the whisks of the hand mixer.
Heat while stirring constantly until the mixture rises in the pot and becomes creamy. Immediately pour from the pot into a bowl and allow to cool slightly. Spread champagne sabayon over the melon wedges and serve decorated with mint, lemon spiral and melon pieces as desired.