Instructions

for the cake

Adjust oven rack to middle position and heat oven to 350 degrees. Grease three 8-inch round cake pans, line with parchment paper, grease parchment, and flour pans. Combine 4 large eggs plus 2 large yolks, ½ cup buttermilk, and 1 tablespoon vanilla extract in 2-cup liquid measuring cup and beat with fork until smooth.
Combine 2¼ cups (9 ounces) cake flour, 1¾ cups (12¼ ounces) granulated sugar, 1¼ teaspoons baking powder, ¼ teaspoon baking soda, and ½ teaspoon table salt in bowl of stand mixer. Fit mixer with paddle and mix on low speed until combined, about 20 seconds. Add 8 tablespoons softened unsalted butter and ½ cup vegetable oil and mix on low speed until combined, about 30 seconds. Increase speed to medium and beat until lightened, about 1 minute. Reduce speed to low and, with mixer running, slowly add egg mixture. When mixture is fully incorporated, stop mixer and scrape down bowl and paddle thoroughly. Beat on medium-high speed until batter is pale, smooth, and thick, about 3 minutes. Divide batter evenly among prepared pans and smooth tops. Gently tap pans on counter to release air bubbles.
Bake cakes until toothpick inserted in center comes out with few crumbs attached, 20 to 25 minutes, switching and rotating pans halfway through baking. Let cakes cool in pans on wire rack for 15 minutes. Remove cakes from pans, discarding parchment, and let cool completely on rack, about 2 hours. (Cooled layers can be wrapped tightly with plastic and stored at room temperature for up to 24 hours).

for the pudding

Meanwhile, whisk 2 tablespoons granulated sugar, 1½ tablespoons Dutch-processed cocoa powder, 1½ tablespoons cornstarch, and ⅛ teaspoon table salt together in large saucepan. Whisk in ⅔ cup whole milk and ¼ cup heavy cream until smooth. Cook over medium heat, whisking constantly, until mixture is thickened and bubbling over entire surface, 3 to 5 minutes. Off heat, whisk in 2 ounces finely chopped bittersweet chocolate until melted and fully incorporated.
Transfer pudding to large bowl. Place plastic wrap directly on surface of pudding and refrigerate until well chilled, at least 2 hours. (Pudding can be refrigerated in airtight container for up to 3 days.)

for the syrup

Bring ⅓ cup (2⅓ ounces) granulated sugar and ⅓ cup water to boil in small saucepan over high heat and stir until sugar is dissolved, about 1 minute. Let cool completely, about 30 minutes.

for the buttercream

Using clean, dry mixer bowl and whisk attachment, whip 20 tablespoons (2½ sticks) softened unsalted butter in stand mixer on medium-high speed until smooth, about 20 seconds. Add 2½ cups (10 ounces) confectioners’ sugar and ⅛ teaspoon table salt and mix on medium-low speed until most of sugar is moistened, about 45 seconds. Scrape down bowl; add 2 tablespoons heavy cream and whip on medium-high speed until light and fluffy, about 4 minutes, scraping down bowl as needed. Add 1 tablespoon grated lemon zest plus ¼ cup juice and whip until incorporated, about 30 seconds. (Frosting can be refrigerated for up to 2 days. If refrigerated, let stand at room temperature for 30 minutes before using).
Transfer fully cooled cakes to cutting board. Using long serrated knife, cut 1 horizontal line around sides of each layer; then, following scored lines, cut each layer into 2 even layers. Place 1 cake layer on 8-inch cardboard round, cut side up. Using pastry brush, gently dab syrup onto cake until evenly moistened, about 1½ tablespoons. Spread ⅓ cup chocolate pudding evenly over top, leaving ¼-inch border around edge of cake. Top with second cake layer (cut side up). Repeat brushing with syrup and spread ⅓ cup lemon curd over top, leaving ¼-inch border. Repeat with 3 more layers, alternating pudding and lemon curd and ending with layer of pudding. Place remaining cake layer cut side down over pudding. 
Using offset spatula, spread all of buttercream evenly over sides and top of cake. Refrigerate cake for 1 hour.

for the ganache

Place 8 ounces finely chopped bittersweet chocolate in 4-cup liquid measuring cup or bowl. Bring 1 cup plus 2 tablespoons heavy cream, 1 tablespoon corn syrup, and ⅛ teaspoon table salt to simmer in small saucepan over medium heat, 1 to 2 minutes. Pour cream mixture over chocolate and let stand for 1 minute. Whisk mixture until thick and smooth. 
Remove cake on cardboard round from refrigerator and place on wire rack set in parchment paper–lined rimmed baking sheet. Working quickly, pour ganache over top of chilled cake (starting in center of cake), letting ganache drip down and coat sides of cake (allow excess ganache to puddle onto baking sheet). Refrigerate cake on rack until ganache is set, about 20 minutes. Using large spatula(s), transfer cake on cardboard round to platter or large cutting board and serve. (Wrap leftover cake in plastic and refrigerate; bring to room temperature before serving.)