Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish.

Combine cake mix, water, 3 eggs, and oil in a large bowl; beat with an electric mixer until well combined, about 2 minutes. Pour batter into prepared baking dish. Set aside.

To make the ricotta cheese layer: Combine ricotta cheese, sugar, vanilla, and remaining 4 eggs in a separate bowl; blend well. Spread ricotta mixture evenly over the top of the cake batter.

Bake in the preheated oven until or toothpick inserted in the center comes out clean, about 1 hour 15 minutes if using a glass baking dish, or 1 1/2 hours if using a metal pan. Allow cake to cool completely before topping.

To make the topping: Blend pudding mix and milk until thickened. Blend in whipped topping. Spread over cooled cake.