Boil the sugar with a glass of water for 2 minutes, then let it cool down. Squeeze the limes. Mix the avocado meat with the lime juice, a little grated lime zest and the sugar syrup. Add the vanilla and rum.
Pour into an ice cream maker and process into a creamy sorbet. Alternatively, place in a flat stainless steel bowl and freeze in the deep-freeze compartment, mashing through with the mixer every hour.
Serve in small balls as an intermediate course. Can be served solo, but also tastes great in combination with raspberry sauce.