1. Cut the two melons in half and hollow them out. Using a melon baller, make balls from the flesh of one melon. Set aside.
2. Remove all the flesh from the second melon and put it in the bowl of a food processor. Add the sugar and mint, and mix well. Add the white wine and blend until the mixture is smooth. Refrigerate until serving time.
3. Wrap the slices of prosciutto around the grissini.
4. To serve, pour the soup into small bowls. Serve with the prosciutto-wrapped grissini and garnish with fresh mint.
Note: Use a dry but fruity white wine, such as an Alsatian or Loire Valley wine.