Gently simmer the chanterelles in a mixture of half & half and heavy cream for about 5 minutes.  Blend the mixture with a stick blender until smooth.  

Separate 6 eggs, reserving the whites for another use.  Whip the egg yolks, and slowly pour a bit of the hot cream mixture into the yolks, whisking constantly.  Add a bit at a time until it's all incorporated.

Transfer the mixture back to a saucepan, and add in the remaining ingredients. Cook on very low heat until it thickens enough to coat the back of a spoon.

Refrigerate until cold, and then freeze the cold custard in an ice cream maker following the manufacturers' instructions.