Preheat your oven to 350°F (175°C) and grease a 9×13-inch baking dish with cooking spray. Set it aside to be ready for the batter.
In a large mixing bowl, beat together the ricotta cheese, sugar, and vanilla extract using an electric mixer until smooth.
Gradually add the 4 large eggs, mixing well after each addition.
In another bowl, whisk together the chocolate cake mix, canola oil, water, and the remaining 3 large eggs until you have a smooth batter.
Pour the chocolate cake batter evenly into your prepared baking dish, and then carefully pour the ricotta mixture over the top, spreading it evenly.
Bake in the preheated oven for 1 hour to 1 hour and 10 minutes. The cake is done when it is fully set and a toothpick comes out clean.
Let the cake cool completely at room temperature.
For the frosting, whisk together the instant chocolate pudding mix and cold milk in a large bowl until it thickens, about 2–3 minutes.
Gently fold in the thawed whipped topping until fully combined.
Spread the pudding frosting evenly over the cooled cake. Cover and refrigerate for at least 4 hours (or overnight) before serving.