Split the watermelon in half, reserving the other half for a later use. Using a large spoon, remove the fruit from the halved watermelon. Using your hands and knife, remove all seeds from watermelon and discard.
Dice watermelon into 2 inch pieces and put in a large bowl with the juice.
In a large saucepan over medium heat, combine heavy cream and sugar. Bring the mixture up to a simmer. Remove from heat.
Whisk the egg yolks until smooth and temper into the hot cream mixture. To temper, slowly add a few spoonfuls of the hot cream mixture to the egg yolks as you whisk. If you stop whisking or add in too much hot cream it will curdle the eggs. Go slowly!
Cook the egg mixture for four minutes or until the mixture coats the back of a spoon. Remove from the heat.
Pour hot cream mixture over watermelon pieces and mix thoroughly. Cool to room temperature.
Using a hand held blender, puree the mixture until smooth and strain through a mesh strainer.
Add the ice cream mixture to your ice cream machine and follow the ice cream machine directions.
Pour the set ice cream into a freezer safe container and chill in the freezer for 2-3 hours until firm set.
The ice cream will keep in a freezer safe airtight container for 2-3 months.If you choose to substitute the heavy cream for milk the resulting custard will be thinner and the ice cream will be more icy. If you are going to substitute it I would not substitute it for anything less than heavy milk. Higher fat content means creamier ice cream.