In a small saucepan, stir the water and sugar together over medium heat until the sugar dissolves. Remove from the heat and let cool.
Peel, pit, and cube the avocados and put them in the bowl of a food processor. Add the sugar water, lime juice and rind, and honey. Blend until pureed.
Transfer the mixture to a metal baking dish, cover, and freeze.
When ready to serve, break the sorbet up into rough pieces with a dull knife and blend again in the food processor. Scrape the mixture into small dessert bowls and serve immediately.
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