Prepare the Brownie Base: Preheat oven to 350°F (175°C). Grease and flour an 8x8 inch baking pan. In a medium bowl, whisk together flour, granulated sugar, cocoa powder, baking powder, and salt. In a separate bowl, whisk the egg, vegetable oil, and vanilla extract. Add the wet ingredients to the dry ingredients and mix until just combined. Pour the batter into the prepared pan and bake for 20-25 minutes, or until a toothpick inserted into the center comes out with moist crumbs. Let the brownie base cool COMPLETELY on a wire rack. This initial cooling step is critical for ensuring a stable foundation.

Make the Chocolate Pudding Layer: In a medium saucepan, whisk together the milk, granulated sugar, cocoa powder, and cornstarch until smooth. Cook over medium heat, stirring constantly, until the mixture thickens significantly and comes to a boil. Remove from heat, then stir in the vanilla extract and butter until melted and combined. Pour the hot pudding evenly over the cooled brownie base, spreading gently. Refrigerate for at least 1 hour, or until thoroughly chilled and firm to the touch. This firm pudding layer creates a solid barrier for the next.

Assemble the Chocolate Mousse Layer: In a microwave-safe bowl, gently melt the chocolate chips in 30-second intervals, stirring until smooth. Let cool slightly. In a separate bowl, whip 3/4 cup of the heavy cream until soft peaks form. In another bowl, whisk the remaining 1/4 cup heavy cream, powdered sugar, and vanilla extract until smooth. Stir the slightly cooled melted chocolate into this cream mixture until well combined. Gently fold in the whipped cream until no streaks remain. Spread this mousse evenly over the chilled pudding layer. Refrigerate for at least 2 hours, or until the mousse is completely set. Proper chilling here is the secret to getting clean, defined layers when you slice.

Create the Whipped Cream Topping: In a cold bowl, whip the heavy cream, powdered sugar, and vanilla extract until stiff peaks form. Spread evenly over the set chocolate mousse layer.

Garnish and Serve: Using a vegetable peeler or grater, create chocolate shavings from the chocolate bar and sprinkle them generously over the whipped cream. Refrigerate the entire dessert for at least 30 minutes before serving. For the cleanest possible slices, run a sharp knife under hot water, wipe it dry, and then make each cut. Reheat and wipe the knife between slices to keep those layers looking absolutely perfect.