Place sugar and zest into Thermomix bowl and mill 10 sec/speed 10.
Add remaining ingredients and blend 30 sec/speed 7. Scrape down sides and repeat if necessary.
Pour into flat baking tray and freeze for several hours.
Cut into chunks and return to Thermo bowl and blend 2 min/speed 8 with the help of the spatula. Serve immediately or keep in freezer until use. You will need to place ice cream in fridge for at least 20 minutes prior to serving as the avocado content makes for a very dense solid ice cream.