Prepare the Cake: Preheat oven to 350°F. Coat 3 (8-inch) round cake pans with nonstick baking spray. Beat together eggs, sugar, and vanilla in the bowl of an electric stand mixer fitted with the whisk attachment on high speed until light and fluffy, about 10 minutes. Remove bowl from mixer, and fold in flour, being sure not to deflate the batter.

Divide cake batters evenly among prepared cake pans; bake in preheated oven on the middle rack until golden, 20 to 22 minutes. Cool completely; transfer to a wire rack, or wrap in plastic wrap and freeze until ready to assemble. 

Prepare the Coffee Soak: Stir together coffee and coffee liqueur. Set aside.

Prepare the Frosting: Beat together mascarpone and cream cheese in the bowl of an electric stand mixer fitted with paddle attachment, on medium speed until fully combined and no lumps, scraping sides of bowl as needed. Add powdered sugar, and beat on low speed until smooth and combined. In a separate bowl, beat together heavy cream and coffee liqueur on high speed until stiff peaks form, about 5 minutes. Fold mascarpone mixture into whipped cream until fully combined and smooth.

Place 1 layer of cake on a cake stand, and brush with some of the Coffee Soak, being sure to generously soak well, covering the entire top of the cake. Dollop 1/3 of the Frosting onto soaked cake layer, and spread to edge of cake top, until you have a smooth flat layer. Top with the next cake layer, and repeat the soaking and frosting process. Top with third cake layer, and brush with remaining Coffee Soak, then top with remaining Frosting; smooth the top flat. Dust with cocoa. Chill until ready to serve.