Preheat your oven to 350°F (175°C). Lightly grease and flour a 9x13 inch baking dish; set aside.

In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt until well combined.

In a separate medium bowl, whisk together the milk, large eggs, and vanilla extract.

Add the softened unsalted butter to the dry ingredients. Using an electric mixer, beat on low speed until the mixture resembles coarse crumbs.

Gradually add the wet ingredients to the dry ingredients, mixing on low speed until just combined. Increase speed to medium and beat for 2 minutes until the batter is smooth and light.

Pour the cake batter into the prepared baking dish and spread evenly.

Bake for 30-35 minutes, or until a wooden skewer or toothpick inserted into the center of the cake comes out clean.

Remove the cake from the oven and let it cool completely in the pan on a wire rack. This is crucial before adding the pudding layer.

In a medium saucepan, whisk together 1 cup of the whole milk with the cornstarch until a smooth paste forms.

In a separate bowl, whisk together the remaining 2 cups of milk, granulated sugar, and egg yolks.

Pour the egg yolk mixture into the saucepan with the cornstarch mixture. Place the saucepan over medium heat.

Cook, whisking constantly, until the mixture thickens considerably and comes to a gentle boil. Continue to boil for 1 minute, still whisking, to ensure the cornstarch is fully cooked.

Remove the saucepan from the heat. Stir in the softened unsalted butter and vanilla extract until completely melted and smooth.

Pour the hot pudding into a clean bowl. Immediately press plastic wrap directly onto the surface of the pudding to prevent a skin from forming. Chill in the refrigerator for at least 1 hour, or until cold and set.

In a large, chilled mixing bowl (preferably one that has been in the freezer for 10-15 minutes), combine the very cold heavy cream, powdered sugar, and vanilla extract.

Using an electric mixer, beat on medium-high speed until stiff peaks form. Be careful not to overbeat, or the cream will begin to turn into butter.

Once the cake is completely cool, use the handle of a wooden spoon or a large fork to poke holes all over the surface of the cake. This allows the pudding to seep in and moisten the cake.

Pour the chilled vanilla pudding evenly over the poked cake, gently spreading it to the edges with a rubber spatula.

Carefully spread the prepared whipped topping over the pudding layer, creating a smooth, even surface.

Cover the cake loosely with plastic wrap and chill in the refrigerator for at least 2-4 hours, or preferably overnight, to allow the flavors to meld and the cake to fully absorb the pudding.

Slice and serve cold. Garnish each slice with chocolate shavings or fresh berries, if desired, just before serving.