Purée. Combine the mango, ginger, lime and 1/4 cup coconut milk in a food processor or high-speed blender. Purée until smooth, pausing as needed to scrape down the sides. The mixture will go from chunks to a crumbly texture to smooth. If needed, add in extra coconut milk to help the mixture blend.
Serve. Scoop and serve immediately. Or transfer the sorbet to a food storage container,* cover and freeze for up to 3 months.
Notes
Food storage container: This ice cream container is my favorite, but any sturdy freezer-safe sealed container will do. If using a container that is glass or metal, I recommend chilling it before adding the sorbet.