Combine the avocados and 1 cup of the cream in the container of a blender or processor. Add the liquor and whirl until smooth. Refrigerate for 2 hours. Beat the egg yolks with another cup of the cream.
In a saucepan, combine the flour, sugar, and salt and whisk to blend thoroughly. Slowly whisk in the remaining 2 cups of cream and stir over medium heat until slightly thickened. Whisk half the hot mixture into the egg yolks. Pour the mixture back into the pan and stir over medium heat for 1 minute.
Remove from the heat, stir in the vanilla, and chill for 2 hours. Combine the avocado mixture and the egg yolk mixture in the container of an ice cream machine and process according to the manufacturer's instructions.