1In 2-quart saucepan, heat half-and-half, milk, cocoa and chocolate chips to simmering over medium heat, stirring with whisk until chocolate is melted. Remove from heat.
2In large bowl, beat egg yolks with whisk until lightened. Gradually add sugar, beating until blended. Gradually add warm milk mixture, stirring until combined. Return mixture to saucepan. Cook over low heat, stirring constantly, until mixture thickens, coats back of spoon and reaches 170°F. Remove from heat; stir in vanilla. Cool 30 minutes. Refrigerate until cold, at least 3 hours or up to 24 hours.
3Pour mixture into ice-cream freezer and freeze according to manufacturer’s directions. Meanwhile, place cake pieces on cookie sheet; freeze 20 to 30 minutes.
4Stir cake pieces into ice cream; swirl in frosting. Transfer to freezer container. Cover; freeze 2 hours or until serving time.