Preheat the oven to 350 degrees F (175 degrees C). Coat a 9x13-inch baking pan with cooking spray.

Combine brownie mix, vegetable oil, eggs, and water in a large bowl. Mix with a wooden spoon until well blended. Spread into the prepared baking pan.

Bake in the preheated oven until a toothpick inserted 2 inches from the side of the pan comes out clean, 22 to 25 minutes. Let cool completely, about 30 minutes.

Meanwhile, combine cream cheese, powdered sugar, and coffee in a large bowl. Beat with an electric mixer until smooth. Beat in 1 cup whipped topping. Spread over cooled brownies and refrigerate while preparing pudding.

Whisk milk and instant chocolate pudding in a large bowl until smooth, about 2 minutes. Let stand until slightly thickened, about 5 minutes.

Spread pudding over the cream cheese layer. Spread remaining whipped topping over the pudding layer. Garnish with walnuts, chocolate shavings, and espresso powder. Refrigerate until ready to serve.