Preheat the oven to 350 degrees F. Grease and flour a 9-by-13-inch baking pan.
Prepare the cake batter according to the package directions. Spoon evenly into the prepared pan. Set aside.
Combine the ricotta, 4 ounces of the mascarpone, sugar, vanilla and eggs in a stand mixer fitted with the paddle attachment. Beat until smooth. Gently scoop the filling onto the batter and spread so the top is completely white.
Bake until a skewer inserted into the center of the cake comes out clean and the spice cake layer has risen to the top, 50 to 60 minutes. Let cool completely in the pan on a cooling rack.
Combine the instant pudding, milk and the rest of the mascarpone in a stand mixer. Beat until thick and smooth. Spread the frosting evenly over the entire cake.