Chocolate Cake with Whipped Fudge Filling and Chocolate Buttercream

Heat the oven to 350°F and arrange a rack in the middle.

Cut out 2 (8-inch) rounds of parchment paper; set aside. Coat 2 (8-inch) cake pans with butter, place the rounds in the pans, and coat the parchment with more butter. Coat the pans and parchment with flour and tap out any excess; set aside.

Whisk together the measured flour, baking soda, and salt in a medium bowl until combined; set aside.

Whisk together the cocoa and boiling water in a small bowl until combined. Slowly whisk in the milk; set aside.

Place the measured butter in the bowl of a stand mixer fitted with a paddle attachment and beat on medium-high speed until fluffy and light in color, about 3 minutes.

Add the sugar and vanilla and continue to beat for another 4 minutes. Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.Return the mixer to medium-high speed.

Add the eggs 1 at a time, letting each incorporate fully before adding the next. Stop the mixer and scrape down the sides of the bowl and the paddle.

Add a third of the flour mixture and turn the mixer to low speed, mixing until the flour is just incorporated.

Add half of the cocoa mixture and mix until just incorporated. Continue with the remaining flour mixture and cocoa mixture, alternating between each and ending with the flour, until all of the ingredients are incorporated and smooth. Stop the mixer, remove the bowl, and stir in any remaining flour streaks by hand, making sure to scrape the bottom of the bowl.Divide the batter evenly between the prepared pans.

Bake them side by side on the rack for 15 minutes. Rotate the pans from left to right and back to front and continue baking until the cake edges slightly pull away from the pans and a cake tester or toothpick inserted into the center comes out dry with just a few crumbs, about 15 to 20 minutes more.

Remove the pans from the oven and let them cool on a wire rack for about 15 to 20 minutes. Run a knife around the perimeter of each cake, turn them out onto the rack, and slowly peel off the parchment rounds.

Let cool completely, about 1 1/2 hours. Meanwhile, make the buttercream and filling.For the milk chocolate buttercream:Fill a medium saucepan with 2 inches of water and bring it to a boil over high heat. Reduce the heat to low so the water is just simmering.

Place the milk and bittersweet chocolates in a heatproof bowl large enough to sit over the water without touching it.

Place the bowl over the saucepan and stir until the chocolate is melted and smooth. Set aside until cooled slightly but still pourable, about 5 to 10 minutes.Beat the butter in the bowl of a stand mixer fitted with a paddle attachment on medium-high speed until light and fluffy, about 3 minutes.

Add the milk and beat until incorporated.

Pour in the chocolate and mix until completely incorporated.

Place the chocolate in the bowl of a stand mixer (the bowl must be heatproof); set aside.

Whisk together the cream and corn syrup in a small saucepan and bring to a boil over medium heat.

Pour the cream mixture over the reserved chocolate and whisk until melted and smooth. Refrigerate uncovered, stirring occasionally, until cooled to room temperature, about 45 minutes to 1 hour.

Place 1 cake layer on an upside-down cake pan or serving plate. Working quickly, spread all of the whipped fudge filling evenly over the top of the layer, then place the second cake layer on top, top-side down. (If the whipped fudge starts to set in the bowl, stir vigorously until smooth.)Using an offset spatula or a long, thin knife, spread the buttercream evenly over the top and sides of the cake. (If the buttercream seems too soft, refrigerate until stiffer but not hard. You can save about 3/4 cup to use for additional decorating, if you like.)To make the decorative chocolate drizzle, use a dark marker or pen to draw 2 parallel lines 14 inches long and 4 inches apart on a sheet of parchment paper. Repeat with a second set of lines on the same sheet of parchment. Flip the parchment over, place it on a baking sheet, and place the baking sheet in the freezer.Fill a medium saucepan with 2 inches of water and bring it to a boil over high heat. Reduce the heat to low so the water is just simmering.

Place the chopped chocolate in a heatproof bowl large enough to sit over the water without touching it, place the bowl over the saucepan, and stir until the chocolate is melted and smooth.

Remove the baking sheet from the freezer. Using a spoon, drizzle a thin stream of chocolate in between the 2 sets of lines in random patterns, making 2 (14-by-4-inch) strips of decorative chocolate drizzles. Return the baking sheet to the freezer until the chocolate is just set, about 5 minutes.Working quickly because the chocolate will get soft, carefully peel the chocolate strips off of the parchment and apply them to the sides of the cake, wrapping them around and pressing slightly to get them to adhere. Don’t worry if the strips break, just press them onto the sides of the cake. (If the chocolate starts to soften, place it back in the freezer for a few minutes to harden.)

Serve immediately or refrigerate for up to 2 days. If refrigerated, let the cake sit at room temperature for 1 to 2 hours before serving.