Process ginger in food processor until finely chopped. Add peaches and condensed milk; cover and process until smooth. Add whipping cream and orange juice; blend well. Spoon into 8 or 9-inch square glass or plastic container. Cover; freeze 1 1/2 to 2 hours or until slightly set.
Transfer mixture to medium bowl. With electric mixer, beat until mixture resembles soft-serve ice cream. Cover; freeze 3 hours or until firm.