Preheat the oven to 375 degrees F (190 degrees C). Grease 3 (9-inch) cake pans.

Make cake: Beat 4 egg whites in a glass or metal bowl with an electric mixer until foamy. Continue to beat until stiff peaks form. Lift the beaters straight up: the tip of the peak should curl over slightly. Set aside.

Sift together cake flour and baking powder in a separate bowl; set aside.

Beat butter, sugar, and salt in a separate large bowl with an electric mixer until light and fluffy. The mixture should be noticeably lighter in color. Add egg yolks one at a time, mixing well after each addition. Pour in cake flour mixture alternately with 1 cup milk, mixing until just incorporated. Stir in lemon juice and vanilla until incorporated.

Whisk beaten egg whites a few times; use a whisk or rubber spatula to fold 1/3 of the egg white mixture into batter to lighten it. Fold in remaining egg whites, mixing just until combined. Pour batter into the prepared pans and spread evenly.

Bake in the preheated oven until cake is light golden brown and just pulling from the sides of the pan, 15 to 20 minutes. Do not overbake. Cool in the pans for 5 minutes, then invert onto wire racks to cool completely.

Make custard: Combine 1 1/2 cups sugar, salt, flour, cornstarch, and cocoa powder in a saucepan and mix well. Whisk remaining 1/2 cup sugar into 4 beaten eggs in a medium bowl; set aside. Pour milk into sugar mixture in the saucepan and cook over medium heat, stirring constantly, until mixture begins to boil. Remove from heat and gradually pour hot milk mixture into egg mixture, whisking constantly. Add chopped chocolate and stir until chocolate melts.

Return custard to the saucepan and cook, stirring constantly, over medium heat until custard is thickened, about 5 minutes. Remove from heat; stir in butter and vanilla. Transfer custard to a bowl and allow to cool.

Make buttercream: Place butter in a large bowl. Gradually beat in confectioners’ sugar until incorporated. Beat in cocoa powder until well combined. Mix in vanilla until smooth. Drizzle in 1 tablespoon hot water or as needed to thin frosting; mix well until desired consistency is reached.

Make ganache: Place chocolate chips in a large bowl. Heat heavy cream in a saucepan until very hot but not boiling. Remove from heat and pour over chocolate chips. Let stand for 3 minutes, then whisk, scraping sides and bottom of the bowl, until smooth. Stir in vanilla. Allow to cool to room temperature; cover and set aside. Ganache should be spreadable and not firm.

Assemble cake: Using a long serrated knife and a gentle sawing motion, slice each cake layer in half horizontally. Cover cake plate with strips of parchment paper or aluminum foil for easier clean up. Put a dab of buttercream in the center of the plate to keep cake from shifting. Set a cake half on the plate.

Spread custard filling onto cake layer, taking care not to spread it too close to the edge (weight of the cake layers will cause it to spread out). Gently lay another cake round on top of the first and repeat with another custard layer. Repeat with remaining layers and custard, topping custard with the last cake layer. Chill cake in the refrigerator for 30 minutes to firm up.

Frost the top and sides of cake with chocolate buttercream. Chill in the refrigerator for 30 minutes to firm and set.

Spread frosted cake with ganache. Remove parchment strips or aluminum foil from the cake plate. Store cake in the refrigerator.