Add the butter and sweetener to a medium saucepan. Heat on medium until melted. Add the walnuts and cook for about 5-8 minutes until the syrup begins turning brown and the nuts smell toasted. Remove from the heat. Stir every 5 minutes as they cool. The syrup will continue to thicken. Once they are well coated and room temperature transfer to a waxed paper lined baking sheet. Refrigerate until the coating is hard.
Meanwhile, put all the ice cream ingredients in a blender. Blend until smooth. Pour into an ice cream machine and freeze according to the manufacturer’s instructions. When the ice cream has finished churning gently stir in the candied walnuts. Freeze until firm.
*** If you are concerned about using raw egg yolks you can purchase pasteurized eggs or you can temper the ice cream base.Notes on Sweeteners: