Place the ice cream maker bowl in the fridge to freeze for several hours before starting to prepare the ice cream.
In a blender, combine the coconut milk, sugar, sea salt, and vanilla. Blend until smooth, about 30 seconds. (You can also mix by hand, but blending will give a smoother texture.)
Pour the mixture into your ice cream maker and churn according to the manufacturer’s instructions. It should thicken to soft-serve consistency in about 20–25 minutes.
Pour half of the coconut ice cream into a loaf pan or freezer-safe container. Drizzle half of the caramel sauce over the top, then swirl gently with a knife. Add the remaining ice cream on top and repeat the process with the remaining caramel sauce.
Freeze the ice cream for at least 6 hours or overnight.