Put the peeled chopped kiwis in the freezer 1/2 hour before pureeing them. Put the chilled kiwis in to a blender along with the sweetener of choice, if using. Blend to a puree.
With the motor running, pour in the olive oil to somewhat emulsify and pour the entire mixture in to the bowl of your ice cream machine.If necessary, based on your ice cream maker's instructions, chill the bowl ahead of time. My ice cream maker has a built in compressor so I typically skip this step. Chill and enjoy!