Brown-sugar buttercream covers a three-tiered cake of buttery brown-sugar pound cakes.
Heat oven to 325 degrees. Butter and flour two 8-by-3-inch square cake pans. Line with parchment paper; set aside.
In a bowl, sift together flour, salt, and baking powder; set aside. In the bowl of an electric mixer fitted with the paddle attachment, combine butter and light-brown sugar. Beat on medium high until fluffy, about 10 minutes. Add eggs one at a time, beating well after each. Add flour mixture to egg mixture, alternating with milk in three additions, beginning and ending with the flour. Stir in vanilla extract.
Pour batter into prepared pans. Smooth the tops; bake until a cake tester inserted in center comes out clean, about 90 minutes. Rotate pans after 45 minutes to promote even baking. Transfer to a cooling rack. Let cool in pans 10 minutes. Remove from pans; let cool completely while making brown-sugar-meringue buttercream.
Assemble cake: using a serrated knife, trim cakes so each is level, even, and about 2 inches high. Cut one cake into a 6-inch square; set aside. Reserve excess cake for another use. Cut second cake into two smaller squares, one 3 3/4 inches and the other 2 1/4 inches. Brush top and sides of each cake with a pastry brush to remove crumbs; set aside.
From a sturdy piece of cardboard, or 3/16-inch foam board, cut out one cake board for each layer. Place trimmed layers onto their corresponding boards. Using an offset spatula, coat each cake with a thin layer of buttercream to seal in the crumbs. Chill in the refrigerator until firm, about 20 minutes. Transfer 3/4 cup buttercream to a pastry bag fitted with a number 5 plain round tip; set aside. With remaining buttercream, cover each layer with a final coat of buttercream, using an offset spatula to smooth the icing. Place cakes in refrigerator to set, about 20 minutes.
Loosen the middle-size cake from its base; carefully center it on the larger cake. Repeat with smallest cake. Pipe dot design on cake; chill if not serving immediately. Remove from refrigerator at least 30 minutes and up to 3 hours before serving.