Make the Cake
Preheat the oven to 300°F.
Lightly grease and flour two 8-inch round cake pans.
1 1/2 sticks (12 tablespoons) unsalted butter, softened
1 cup light brown sugar
1 cup granulated sugar
In the bowl of an electric mixer, cream the butter and sugars.
2 large eggs, plus 1 yolk
Add the eggs and yolk and combine.
1 1/2 cups all-purpose flour
2/3 cup unsweetened cocoa powder, sifted
2 teaspoons baking powder
1 teaspoon baking soda
Whisk the remaining dry ingredients together, in a separate bowl.
1 cup pumpkin puree
1/2 cup buttermilk
2 teaspoons vanilla extract
Whisk the pumpkin puree together with the buttermilk and vanilla in another bowl.
Alternate mixing dry ingredients with the pumpkin mixture into the egg mixture. Start with dry and end with wet.
Divide the batter between the prepared cake pans.
Bake for 30 to 40 minutes, until a toothpick inserted in the middle comes out clean.
Let the cakes cool and unmold.
Make the Frosting
8 ounces cream cheese, softened
1/2 stick (4 tablespoons) unsalted butter, softened
In the bowl of an electric mixer, cream the cream cheese and butter together until soft.
4 cups confectioners' sugar
Add the confectioners' sugar, blending in 1 cup at a time.
1/2 cup whole milk
Add the milk slowly, as needed, and mix until the frosting is smooth and creamy.
Make the Glaze
1/2 cup heavy cream
3 tablespoons light corn syrup
1 tablespoon unsalted butter
Heat the heavy cream, corn syrup, and butter in a saucepan until boiling.
1/2 cup semisweet chocolate chunks (52–62% cacao)
Place the chocolate in a bowl.
Pour the cream mixture over the chocolate until it is completely melted, mixing gently with a rubber spatula until the glaze is smooth.
Assemble the Cake
Slice each cake in half with a long serrated knife to create 4 thin layers.
Place 1 bottom layer on a cake plate.
Ice the top with 3 to 4 tablespoons frosting and repeat with the remaining layers.
You will have a 4-layer unfrosted cake.
Then use a cake spatula to mask the top and sides until the cake is evenly frosted.
Set it in the fridge for 10 minutes.
Then remove the cake from the fridge and pour the chocolate glaze over the center of the cake until the top is covered and the glaze runs over the sides, still showing some frosting.
Let the glaze set and serve.