2 sticks (1 cup) unsalted butter, room temperature, plus more for pans
1 1/2 cups all-purpose flour, plus more for pans
1 1/2 cups cake flour (not self-rising)
1 tablespoon baking powder
1/2 teaspoon salt
1 3/4 cups sugar
4 large eggs
2 teaspoons pure vanilla extract
1 1/4 cups milk
Preheat oven to 350 degrees. Butter two 9-by-2-inch round cake pans; line the bottoms with parchment paper. Butter parchment, and dust with flour, tapping out excess; set aside. Into a medium bowl, sift together flours, baking powder, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar until light and fluffy, 3 to 4 minutes, scraping down the sides of the bowl as needed. Beat in eggs, one at a time, then beat in vanilla. With the mixer on low speed, add the flour mixture in three parts, alternating with the milk and beginning and ending with the flour; beat until combined after each addition.
Divide batter between the prepared pans, and smooth with an offset spatula. Bake, rotating the pans halfway through, until cakes are golden brown and a cake tester inserted into the center comes out clean, 30 to 35 minutes. Transfer pans to a wire rack to cool 20 minutes. Invert cakes onto the rack; peel off the parchment. Reinvert cakes and let them cool completely, top sides up.
24 ounces best-quality semisweet chocolate, finely chopped
1/2 cup plus 1 tablespoon Dutch-process cocoa powder
1/2 cup plus 1 tablespoon boiling water
3 sticks (1 1/2 cups) unsalted butter, room temperature
1/2 cup confectioners' sugar
Pinch of salt
Place chocolate in a heatproof bowl set over (but not touching) simmering water. Turn off heat; stir occasionally until chocolate has melted completely, about 15 minutes. Set bowl on countertop, and let chocolate cool to room temperature, 25 to 30 minutes. Meanwhile, combine cocoa powder and boiling water in a small bowl; stir until cocoa is dissolved.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter, confectioners' sugar, and salt on medium-high speed until light and fluffy, 3 to 4 minutes. Add melted chocolate; beat on low speed until combined, 1 to 2 minutes, scraping down the sides of the bowl as needed. Beat in cocoa mixture.
Using a serrated knife, trim tops of cakes to make level; brush off crumbs. Place four strips of parchment paper around perimeter of a serving plate or lazy Susan. Place the first layer on the cake plate, and spread top with 3/4 cup of frosting. Place the second layer on top, bottom side up, and spread top with 3/4 cup of frosting; repeat process with the third layer. Place the remaining layer on top of the third layer, bottom-side up; insert a dowel into the center of cakes if necessary. Spread entire cake with remaining frosting. Decorate with sprinkles, if desired.