Spray a 9×13-inch cake pan with nonstick cooking spray.

In a large bowl, combine the cake mix, coffee, eggs, and oil. Beat the cake batter according to the package directions and set aside.

In a second large bowl, combine the ricotta, eggs, sugar, and vanilla extract. Beat with a hand mixer on low speed until the mixture is homogeneous, about 1 minute. Scrape the sides of the bowl and ensure everything is fully mixed.

Scrape the cake batter into the bottom of the prepared cake pan in an even layer. Spoon the ricotta mixture over the chocolate cake batter, starting at the edges and working your way to the middle. Use an offset spatula to spread the ricotta filling into an even layer, fully covering the cake batter.

Bake the cake until the chocolate cake layer has risen to the top of the cake and a knife inserted into the center comes out clean, 45 to 60 minutes. The ricotta mixture may stick to the knife slightly but shouldn’t be wet. Cover the cake with foil in the last 15 minutes of baking if you notice the edges overbrowning.

Place the cake on a cooling rack and cool until the pan is no longer warm, 1 1/2 to 2 hours.

In a clean large bowl, whip the cold heavy cream on medium speed to stiff peaks, about 2 to 3 minutes, and set aside.

Pour the pudding mix into a medium bowl and whisk to remove any clumps. Pour in the cold milk and whisk until smooth and thick, about 2 minutes.

Fold half of the whipped cream into the pudding mixture. Once the first half has been incorporated, fold in the remaining whipped cream. The mixture should be completely homogeneous and fluffy.

Spread the chocolate topping evenly over the cooled cake. Cover in plastic wrap and refrigerate until fully chilled, at least 5 hours or overnight.

Once the cake is thoroughly chilled, cut into squares and serve. Store leftovers covered in the refrigerator for up to 5 days.