Place the bowl of your ice cream maker in the freezer overnight – or for at least 12 hours.
Peel your ginger root and chop it into small pieces, somewhere in between dicing and mincing. Combine the ginger, mint leaves, sugar, and water in a small sauce pan and bring to a boil over medium/high heat. Reduce the heat to low and simmer for 5 minutes. Make sure to stir it at least once a minute. Remove the saucepan from the burner and allow to cool for five minutes. Once cooled, strain the mixture through a cheesecloth (you can use a fine mesh sieve – or just scoop out the mint leaves and ginger pieces using a spoon if you chopped them big enough).
In a food processor, combine watermelon, ginger mint syrup, and the juice from half a lime. Process until the watermelon is completely broken down. Add in the heavy cream and process gently – if you do it too long the mixture might start developing whipped cream peaks.
Pour the mixture into your ice cream maker and churn for about 20 minutes. Transfer to a loaf pan lined with parchment paper or an ice cream container and freeze for at least two hours or until solid!