If the weather is cool, the fat in the coconut milk will usually be solid. The coconut milk for 20 seconds to melt the coconut solids, and then whisk it.
Combine the coconut milk and the well shaken heavy whipping cream, I like putting them into a large glass measuring cup (4 cup) because the spout makes it easy to pour, but any medium-size mixing bowl will do.
Pour the mixture into your ice-cream maker and process according to your machine's directions. For my Cuisinart Ice Cream Maker, it takes about 20 minutes of churning to produce slightly harder than soft serve ice cream.
Transfer the ice cream into a glass container. Cover with aluminum foil, and put in the freezer to set up. If the ice cream has been chilling for more than two hours, it may be quite hard when you remove it from the freezer. That's okay, you can just let it sit out for a few minutes before scooping, or if you're like me and too impatient to wait, you can remove the foil and microwave it for 30 seconds.