Bring the water, sugar, and ginger to a boil in a small pot until the sugar has dissolved. Bash the ginger around with a blunt object. Allow the syrup to cool and the ginger to infuse further.
Strain the syrup into a bowl and add the coconut milk, miso paste & crystalized ginger, and ginger syrup. Whisk to ensure the miso is thoroughly incorporated. Add a teaspoon of lime juice (optional).
Pour the mixture into the ice cream machine and churn until it is a scoopable consistency. Remove and freeze until ready to serve.
Notes
To make this without an ice cream machine:Pour the cooled mixture into a Ziploc bag. Place the bag on a tray and flatten it out and seal it. Freeze the bag for a few hours or overnight. Once frozen, remove from the bag and break into chunks into the bowl of a food processor. Whiz the processor for 30 seconds or until smooth.Scrape down the bowl with a spatula and decant it into a metal container. Smooth the surface and freeze until solid and you are ready to serve.