Cut avocado lengthwise and remove the pit. Scoop avocado into a blender.
To the avocado add coconut milk, heavy cream, and sweetener, then blend until smooth.
Juice and zest the lime. Add both to the blender. Blend ingredients again for one minute. Refrigerate blended ingredients for at least one hour.
Preheat pan over medium heat. Add coconut flakes and toast until lightly brown around the edges, being careful not to burn. Remove pan from heat and set aside.
Transfer the avocado ice cream mix to the ice cream machine and churn according to manufacturer’s directions. Alternately, if no machine is available, freeze in a container with a lid or in an ice cube tray for mini portions. (Once cubes are frozen, transfer to a ziplock bag)
Once the ice cream is ready, sprinkle with toasted coconut flakes to taste and serve.