Cut each cake roll into 6 slices; reserve any broken chocolate coating for topping. Line bottom and sides of a 9-in. springform pan with cake slices, covering completely.
Whisk milk and pudding mixes 2 minutes (mixture will be thick); spread onto bottom layer of cake rolls. Cover with whipped topping. Sprinkle with reserved chocolate pieces. Refrigerate, covered, at least 2 hours before serving.