Beat the egg yolks in a medium bowl, and set aside.
In a medium saucepan, heat the cream, sugar, and salt over medium-high heat, stirring regularly, until the sugar dissolves and the cream starts to come to a simmer (scalding).
Remove the saucepan from the heat, and slowly pour the egg yolks into the scalded cream, stirring constantly as you pour them in. Allow the mixture to cool completely in the saucepan, stirring occasionally, add the vanilla, and chill the custard in the fridge.
Peel and remove the pits of the avocados. In a small bowl, mash the avocados until they are smooth and creamy. Mix the mashed avocado into the chilled custard, and add the lime zest and lime juice. Taste the ice cream mixture for sweetness, and add more sugar if you prefer a sweeter ice cream, as the sweetness will dull a bit when the custard is frozen.
Pour the custard mixture into the bowl of your ice cream machine, and process according to the manufacturer's directions.
Serve the Avocado Lime Ice Cream garnished with lime slices or additional lime zest.