Place the coconut milk, sweetener, coffee, and vanilla, if using, in a saucepan. Heat over medium-low heat while whisking. When very hot to the touch add the rum.
Gently simmer while stirring the mixture for 2 minutes. Remove from the heat and let sit for about 10 minutes.
Pour the coffee mixture into a glass dish. Refrigerate for at least 3 hours to chill completely.
Stir and then process in your ice cream maker according to the manufacturer's directions (make sure you have pre-frozen the machine's container, if needed).
Serve immediately. Pack leftovers into a freezer-safe container and freeze. The rum will keep it from hardening too much.
Recipe by Go Dairy Free at https://www.godairyfree.org/recipes/paleo-coffee-soft-serve-ice-cream