Heat the oven to 350°F. Coat a 9x13-inch baking pan with cooking spray. Line the bottom and two long sides with a sheet of parchment paper.

Prepare 1 (15.25-ounce) box chocolate cake mix by mixing in the water, eggs, and oil as listed on the package directions along with 1 ½ teaspoons instant espresso powder if using. Pour into the baking pan and smooth out the top.

Process 2 pounds whole-milk ricotta cheese, ¾ cup granulated sugar, ⅓ cup packed light brown sugar, 3 large eggs, 2 teaspoons vanilla extract, and ½ teaspoon kosher salt in a food processor until well-combined and smooth, about 30 seconds. Pour evenly over the cake batter, covering the cake batter completely.

Bake until the batters have flipped — the chocolate cake will have risen to the surface — and a tester inserted into the center comes out clean, 1 hour to 1 hour and 10 minutes. It’s OK if the cake has cracks or thin streaks of the ricotta mixture on the surface. Place the pan on a wire rack and let cool completely, about 2 ½ hours.

Whisk 1 (3.9-ounce) box instant chocolate pudding mix and 2 cups cold whole milk together in a large bowl until dissolved and the mixture is slightly thickened, about 2 minutes. Let sit for 1 minute to thicken. Fold 1 (8-ounce) container thawed Cool Whip with a flexible spatula until fully combined.

Spoon over the cooled cake and smooth or swoop over the top as desired. Loosely cover with plastic wrap. Refrigerate until the topping is set and chilled before serving, at least 4 hours and up to overnight.