In the bowl of an electric mixer fitted with a whisk attachment, combine sugar, flour, cocoa, baking powder, baking soda, and salt at medium speed until blended. In another bowl, whisk eggs, milk, oil, and vanilla. Gradually beat egg mixture into flour mixture, about 5 minutes. Shift mixer to low speed; add hot water until blended. Pour batter into pan. Bake until toothpick comes out of the center clean, 20 to 25 minutes. Cool cake completely.
In the bowl of an electric mixer fitted with a whisk attachment, beat egg yolks at medium speed until they become lemon colored and ribbonlike when beaters are lifted, about 5 minutes. Meanwhile, in a small saucepan, combine sugar and 1/4 cup water. Cook over medium-low heat, swirling pan occasionally, until sugar completely dissolves and syrup just comes to a boil. Increase heat to high; boil syrup until it registers 238°F on a candy thermometer. With the mixer on medium speed, immediately add syrup to beaten egg yolks in a thin, steady stream. Beat mixture until it cools to room temperature and is light and fluffy, about 10 minutes. Gradually add butter, 1 tablespoon at a time, until completely incorporated. In a cup, dissolve espresso powder in hot water; beat into buttercream.
In a large bowl, combine chocolate and butter. In a small saucepan, heat cream and sugar over medium-high flame, stirring occasionally, until small bubbles appear around edge of pan. Pour hot cream over chocolate; stir until chocolate and butter melt and mixture is completely smooth. Cool, stirring occasionally, until thickened but not pasty, about 15 minutes.
Invert cake onto a large wire rack; peel off parchment paper. Invert cake again onto a large cutting board. With a serrated knife, cut cake into equal thirds.
Set a large wire rack over a sheet of waxed paper. Arrange one cake layer on rack; spread half of buttercream evenly over top. Add another cake layer; spread top with remaining buttercream. Place remaining cake layer on top.
Pour ganache over top of cake, spreading with a spatula so it coats the sides. If ganache does not cover sides completely, pour any excess that has collected on the waxed paper back into bowl and spread again. Refrigerate cake until ganache sets, about 1 hour. Use two large spatulas to transfer cake onto a serving platter.