Slice open the avocados, remove the pits, and scoop out the flesh. Put the avocados in a blender of food processor. Add the sugar, sour cream, heavy cream, lime juice, and salt. Blend until smooth.

Freeze in your ice cream maker according to manufacturer's instructions. If you like soft ice cream, go ahead and eat. If you like firmer ice cream, store in the freezer for a couple of hours before serving.