Brushing the cake layers with a simple syrup before frosting keeps the cake from crumbling and drying out.
In a saucepan, combine 1/3 cup each sugar and water over medium-high heat and cook, stirring, until sugar dissolves. Remove simple syrup from heat; let cool.
Preheat oven to 425 degrees. Butter two 8-by-2-inch round cake pans. Line bottoms with parchment rounds; butter parchment. In the bowl of a standing mixer fitted with the whisk attachment, combine eggs and remaining 1 cup sugar. Whisk on medium speed until quadrupled in volume and mixture holds a 3-second ribbon, about 10 minutes. Whisk in vanilla.
In a bowl, combine cocoa and flour. Sift over egg mixture; using a large rubber spatula, carefully fold into egg mixture, cutting through center and lifting gently over sides. Divide batter among prepared pans. Bake until cake pulls away from sides of pan and is springy to touch, 15 to 17 minutes. Remove from oven. Run a small knife around sides of pan. Invert onto rack; remove parchment, and re-invert onto rack to cool completely.
Using a serrated knife, trim tops of cakes horizontally to level surface. Halve each cake horizontally to form 2 layers. Transfer 1 layer to a serving platter; generously brush with simple syrup and spread 3/4 cup frosting on top. Set another cake layer on top, and repeat process with remaining simple syrup, frosting, and cake layers. Frost top and sides of cake in a swirling motion. Refrigerate until set, about 1 hour.