Add the melon pulp into the bowl of a food processor and process until smooth. Mix egg yolks with sugar and vanilla until thick, creamy and pale yellow colored. You can do that over a double boiler too. In a separate bowl whip the whipping cream until stiff peaks form. Fold the cream through the egg yolks mixture. Add melon puree and stir to combine. Transfer in a covered storage container and place in the freezer. Freeze for at least 4 hours or overnight. Thaw ice cream 8 to 10 minutes at room temperature before serving.