In a medium saucepan, heat the cream and sugar until the sugar is dissolved. Remove from the heat.
Place the melon and the mint in a food processor and blitz on high until the fruit is completely smooth.
Turn the processor down to the lowest setting and pour the cream onto the melon. Blitz until smooth.
Set up your ice cream machine and start the churn blade.
Pour the melon mix into the ice cream machine and churn for 45 minutes.
Transfer the ice-cream to a freezer proof container and freeze for at least 5 hours before serving.