In a large heavy saucepan, heat half-and-half cream and sugar until bubbles form around sides of pan. Whisk a small amount of hot mixture into the egg. Return all to the pan, whisking constantly.
Cook and stir over low heat until mixture is thickened and coats the back of a spoon. Quickly transfer to a bowl; place in ice water and stir for 2 minutes. Stir in heavy cream, persimmon, pudding mix and spices. Press plastic wrap onto surface of custard. Refrigerate for several hours or overnight.
Fill cylinder of ice cream freezer two-thirds full; freeze according to the manufacturer’s directions. Refrigerate remaining mixture until ready to freeze. Transfer ice cream to freezer containers, allowing headspace for expansion. Freeze 2-4 hours or until firm. Repeat with remaining ice cream mixture.
