1 package instant chocolate pudding
1 1/2 cups flour
2 teaspoons baking powder
1/2 teaspoon baking soda
1/2 teaspoon salt
1 stick (8 tablespoons) unsalted butter
3/4 cup cocoa powder (preferably Dutch-processed)
1 cup water
1 cup buttermilk
1 cup packed light brown sugar
1 cup granulated sugar
2 large eggs
1 teaspoon vanilla extract
Follow instructions on instant pudding packet and make pudding.
For the cake: Adjust an oven rack to the middle position and heat the oven to 325 degrees. Grease and flour 2 8-inch cake pans. Whisk the flour, baking powder, baking soda and salt in a medium bowl.
Melt the butter in a large saucepan over medium heat. Stir in the cocoa powder and cook until fragrant, about 1 minute. Off the heat, whisk in the water, buttermilk, and sugars until dissolved. Whisk in the eggs and vanilla, then slowly whisk in the flour mixture.
Divide batter evenly between prepared pans and bake until toothpick inserted in center comes out clean, 30 to 35 minutes. Cool layers in pans 15 minutes, then invert onto wire rack. Cool to room temperature, at least 1 hour.
To assemble the cake: Cut each cake in half horizontally. Crumble one cake layer into medium crumbs and set aside. Place one cake layer on serving platter or cardboard round. Spread 1 cup pudding over cake layer and top with another layer. Repeat with 1 cup pudding and last cake layer. Spread remaining pudding evenly over top and sides of cake. Sprinkle cake crumbs evenly over top and sides of cake, pressing lightly to adhere crumbs