Four-Layer Chocolate Birthday Cake with Milk Chocolate Ganache and Nutella Buttercream

Preheat oven to 350˚. Butter two 9"-diameter cake pans and line bottoms with parchment paper rounds. Butter parchment and dust with flour, tapping out excess.

Heat chocolate, coffee, and ⅔ cup cocoa powder in a medium heatproof bowl set over a medium saucepan of barely simmering water (water should not touch bottom of bowl), stirring until chocolate melts and mixture is smooth. Let cool, then whisk eggs, buttermilk, and vanilla into chocolate mixture.

Using an electric mixer on low speed, mix salt, baking powder, baking soda, and 2 cups flour in a large bowl just to combine. Add brown sugar, oil, ½ cup butter, and ½ cup reserved chocolate mixture and beat on medium speed until flour is evenly distributed and mixture is smooth, about 2 minutes. Add remaining chocolate mixture in 2 additions, scraping down sides and bottom of bowl as needed and beating until smooth after each addition. Scrape batter into prepared pan and smooth top.

Bake cake until top is firm to the touch and a tester inserted into the center comes out clean, 30–40 minutes. Transfer cake pan to a wire rack and let cake cool in pan 10 minutes before turning out onto a wire rack. Let cool completely.

Using a serrated knife and moving it back and forth in long, even strokes, carefully halve cakes lengthwise.

Place chocolate in a medium bowl. Bring cream and salt to a simmer in a small saucepan over medium-low heat. Pour over chocolate; let sit 10 minutes, then whisk gently until chocolate is melted and mixture is smooth and glossy. Let ganache cool, 30–45 minutes.

Using an electric mixer on medium speed, beat butter into ganache until mixture is light and fluffy and has turned matte, about 3 minutes.

Place 1 cake layer, cut side up, on a platter. Using a rubber spatula, spread one-third of ganache over cake, spreading to edges. Place another cake layer, cut side down, on top and spread another third of ganache over cake. Repeat process once more with another cake layer and remaining ganache; top with remaining cake layer (leave top bare). Chill cake 1–8 hour.

While cake is chilling, beat egg yolks, egg, and salt in the bowl of a stand mixer fitted with the whisk attachment until mixture is pale and thick and falls back onto itself in a slowly dissipating ribbon, about 5 minutes.

Meanwhile, bring sugar and 3 Tbsp. water to a boil in a small saucepan over medium heat, stirring until sugar is dissolved. Clip thermometer to the side of saucepan and boil, swirling pan (do not stir), until thermometer registers 238˚. Immediately remove from heat.

Reduce mixer speed to low and gradually stream hot sugar syrup into eggs aiming for where the egg meets the side of the bowl (this will prevent hot sugar from splattering). Increase speed to high and beat mixture until light and fluffy and sides of bowl are cool to the touch, 5–8 minutes.

Add butter a piece at a time, beating to thoroughly incorporate before adding the next piece and scraping down sides of bowl often. Add Nutella and vanilla and beat, scraping down sides and bottom of bowl, until mixture is smooth and homogenous.

Spread buttercream all over top and sides of chilled cake, making decorative swirls and swooshes. Decorate with sprinkles, if desired.

Do Ahead: Cake can be assembled 1 day ahead. Chill uncovered.