Combine pudding mix and 2 tablespoons cocoa in small bowl. Add milk; beat on low speed of mixer until smooth and thickened. Fold in 1 cup whipped topping, blending well.
Spread about 1 tablespoon pudding mixture onto top of each chocolate wafer; put wafers together in stacks of 4 or 5. On foil, stand wafers on edge to make one long roll. Wrap tightly; refrigerate 5 to 6 hours.
Sift remaining 1 tablespoon cocoa over remaining 2-1/2 cups whipped topping; blend well. Unwrap roll; place on serving tray. Spread whipped topping mixture over entire roll. Remove wrappers from chocolate pieces; place on roll to garnish. To serve, slice diagonally at 45° angle. Cover; refrigerate leftover dessert.