Preheat the oven according to the cake mix directions. Coat a 9-by-13-inch pan with canola oil. Prepare the cake batter according to the cake mix directions, pour into the prepared pan and set aside.
To make the filling: Combine the ricotta, mascarpone, eggs, sugar and salt in the bowl of a stand mixer and whisk until smooth. Gently pour the filling onto the cake pan of chocolate batter so the top is completely white. Bake until a skewer inserted in the center comes out clean and the chocolate layer has risen to the top, about 40 minutes. Let the cake cool completely.
To make the frosting: Just before serving, blend together the mascarpone, milk, chocolate pudding mix and sugar in the bowl of a stand mixer until smooth. Using an offset spatula, spread the frosting evenly over the cake and serve.
Adapted from "One Dish at a Time: Delicious Recipes and Stories from My Italian-American Childhood and Beyond" by Valerie Bertinelli © Rodale 2012. Provided courtesy of Valerie Bertinelli. All rights reserved.