Meanwhile, butter two 9-inch round cake pans, line the bottoms with parchment-paper rounds, and butter the parchment. Sprinkle the pans with flour, tilting them to coat the bottom and sides, then knock out the excess. Into the bowl of a stand mixer, sift the pastry flour, cake flour, baking powder, and salt. Add the sugar, whisk to combine, and set aside.

When the cocoa mixture is cooled, in a 1-quart liquid measuring cup or medium bowl, whisk together the eggs, almond oil, and vanilla. Add approximately one-third of the cocoa mixture and whisk until homogenous.

Make the cake: Adjust an oven rack to the lower-middle position and heat the oven to 350 degrees. Place the cocoa in a small bowl and pour the boiling water or hot coffee over it. Whisk until completely smooth, then let cool to room temperature.

Add the butter and the remaining cocoa mixture to the dry ingredients in the mixer bowl, then attach the bowl to the mixer. Using the flat-beater attachment, mix on low speed until the mixture is evenly moistened, about 1 minute, scraping down the bowl once or twice with a silicone spatula. Increase the speed to medium and beat for about 1½ minutes to build structure in the batter. Scrape down the bowl. With the mixer running on medium-low speed, stream in about one-third of the egg-cocoa mixture and mix until it has been mostly incorporated, then continue to beat for about 30 seconds; scrape down the bowl. Add the remaining egg-cocoa mixture in the same way, in two more batches. Detach the bowl from the mixer and give the batter several folds with the spatula to ensure that it is well combined.

Divide the batter evenly between the prepared pans, then spread into an even layer and smooth the surface. Bake until the cakes are slightly domed and a toothpick inserted into the centers comes out clean, about 30 minutes. Let the cakes cool in the pans on a wire rack for 10 minutes; the domes should level off. Run a paring knife around the edges. Invert each cake onto a wire rack, lift off the pan, and peel off and discard the parchment. Let the cakes cool completely, at least 1½ hours.

While the cakes cool, make the buttercream: Set a fine-mesh strainer over a small bowl. In another small bowl, whisk together the egg yolks and 3.5 ounces of the sugar until well combined. In a heavy-bottomed small saucepan, bring the milk to a bare simmer over medium heat. Gradually whisk the hot milk into the yolk mixture, then return the milk-yolk mixture to the saucepan. Cook over medium heat, stirring constantly, until the custard thickens enough to heavily coat the back of a spoon and reaches 175 to 180 degrees on a digital instant-read thermometer; do not let it reach a simmer. Immediately pour the custard into the strainer. Stir the vanilla and salt into the custard, then let cool to room temperature; occasional stirring will help it cool more quickly.

While the custard cools, fill a medium saucepan with about an inch of water and bring to the barest simmer over medium heat. Place the chocolate in a medium heatproof bowl and set the bowl on the saucepan. Melt the chocolate, stirring occasionally with a silicone spatula, until completely melted and smooth. Remove the bowl from the saucepan and let the chocolate cool to room temperature, stirring occasionally.

When both the custard and chocolate are cooled, in a heavy-bottomed small saucepan, combine the remaining 3.5 ounces sugar and the water; set the pan aside. Place the egg whites in a spotlessly clean large bowl and beat with a handheld mixer on medium-low speed until frothy, about 15 seconds. Add the cream of tartar. At this point, set the saucepan over medium heat and bring the sugar mixture to a simmer, occasionally swirling the pan to help dissolve the sugar. As soon as the syrup reaches a simmer, begin beating the egg whites on medium-high speed and continue to beat until the whites hold soft peaks, no longer. When the sugar syrup registers 245 to 248 degrees, begin to drizzle it into the egg whites as you beat them on medium-high speed, making sure to move the beaters to the areas where the syrup lands. After all the syrup has been added, continue to beat the meringue on medium-high speed until it is glossy, voluminous, and holds soft peaks, about 5 minutes; do not overbeat.

In the bowl of a stand mixer fitted with the flat-beater attachment, beat the butter on medium speed until soft and creamy, 30 to 45 seconds. With the mixer running, slowly pour in the cooled custard and beat until fully incorporated. Scrape down the bowl. With the mixer running on medium speed, add the meringue one heaping spoonful at a time, then beat until homogenous. Scrape down the bowl. With the mixer now running on medium-low speed, slowly pour in the cooled, melted chocolate, then beat until fully combined. Detach the bowl from the mixer and fold with the spatula, scraping along the bottom and sides of the bowl, until the buttercream is uniformly colored.

Assemble the cake: Using a serrated knife, cut each cake in half horizontally, creating a total of four layers. Place a small dab of buttercream on the center of a 9-inch cardboard cake round, then place one of the cake layers crust side down on the cake round. Using an offset icing spatula, evenly spread a heaping ½ cup of buttercream onto the cake layer. Place a second cake layer on top and gently press it down. Spread on a layer of buttercream as you did before. Repeat to build the third layer of cake and buttercream. Place the fourth and final cake layer crust side up on top and gently press down. Now cover the sides and top of the cake with a thin coating of buttercream; this is the “crumb coat” that seals in loose crumbs and prevents them from marring the final coating of buttercream. Refrigerate the cake uncovered for 15 to 20 minutes to set the crumb coat. Frost the bottom and sides of the cake with a thick layer of the remaining buttercream, then use the back of a spoon to create swoops and swooshes in the frosting.