1. Halve the avocados and remove the pit. Scoop out the flesh and put it in a blender or the bowl of a food processor.
2. Add the coconut milk, heavy cream, sugar, rum, salt, and lime juice, and puree until completely smooth. Chill the mixture thoroughly.
3. Once chilled, freeze in your ice cream maker according to the manufacturer’s instructions. Serve scoops garnished with toasted coconut.