Adjust oven rack to middle position and heat oven to 350 F. Grease and flour two 8-inch square cake pans. Combine flour, baking soda, baking powder, and salt in bowl; set aside. In a small bowl, whisk hot water and cocoa powder until smooth; set aside. With electric mixer on medium-high speed, beat butter and granulated sugar until light and fluffy, about 3 minutes. Add eggs, 1 at a time, and mix until incorporated. Add flour mixture in 3 additions, alternating with 2 additions of buttermilk, until combined. Reduce speed to low and slowly add cocoa mixture and vanilla until incorporated.
Scrape equal amounts of batter into prepared pans and bake until toothpick inserted in center comes out with a few crumbs attached, 25 to 30 minutes. Cool cakes in pans 15 minutes, then turn out onto wire rack. Cool completely, about 1 hour. (Cooled, wrapped cakes can be stored at room temperature for 2 days.)
Add 4 tablespoons butter, brown sugar, salt and 1/2 cup evaporated milk in large saucepan over medium heat until small bubbles appear around perimeter of pan, 4 to 8 minutes. Reduce heat to low and simmer, stirring occasionally, until mixture has thickened and turned deep golden brown, about 6 minutes. Transfer to large bowl. Slice remaining butter into 4 pieces and stir in with remaining evaporated milk until mixture is slightly cool. Add chocolate and vanilla and stir until smooth. Whisk in confectioners' sugar until incorporated. Cool to room temperature, stirring occasionally, about 1 hour.
Place 1 cake square on serving platter. Spread 1 cup frosting over cake, then top with second cake square. Generously spread remaining frosting evenly over top and sides of cake. Refrigerate cake until frosting is set, about 1 hour. Serve. (cake can be refrigerated, covered, for 2 days. Bring to room temperature before serving.)