Add the coconut milk, sugar, nutmeg, and cornstarch to a medium-sized saucepan. Whisk together.
On medium/high heat, bring to a boil - stirring occasionally. Once the mixture comes to a boil, reduce heat and let simmer for 15 minutes, continuing to stir occasionally. If the mixture ever stops simmering, turn up the heat slightly.
Remove from heat and put in the refrigerator to cool. Read the manufacturer's directions for your ice cream maker. If the directions indicate the mixture must be cold before freezing then allow the mixture to fully cool.
Add the cooled mixture, vanilla, banana, and salt to the blender. Blend on high for a couple of minutes or until the mixture is smooth and creamy.
Add to your ice cream maker and follow the manufacturer's directions to freeze.
Scoop into a freezer-safe container and continue to freeze.