Preheat the oven to 350°F (175°C). Spray a 9×13-inch baking pan with cooking spray and line it with parchment paper, leaving an overhang on the sides.
Prepare the chocolate cake mix according to the package instructions, then stir in the instant espresso powder if using. Pour the batter into the prepared pan and smooth the top.
In a food processor or blender, combine ricotta cheese, granulated sugar, light brown sugar, eggs, vanilla extract, and salt. Process until the mixture is smooth and well combined.
Gently pour the ricotta mixture over the chocolate batter in the pan, spreading it evenly without stirring.
Bake for 1 hour to 1 hour 10 minutes, or until the top layer appears set and a toothpick inserted in the center comes out clean.
Let the cake cool completely in the pan for about 2 ½ hours.
Whisk together thawed Cool Whip, chocolate pudding mix, and cold milk until thick and fluffy. Spread this mixture evenly over the cooled cake.
Refrigerate for at least 30 minutes before slicing and serving.