Position rack in lower third of oven. Preheat oven to 350 degrees F. Lightly grease sides of 13x9x2-inch baking pan. Line bottom of pan with parchment paper; set aside.
In large mixing bowl whisk together flour, brown sugar, 1/3 cup cocoa powder, baking soda, and salt. Add butter, eggs, and vanilla. Whisk gently until dry ingredients are moistened and mixture resembles a thick paste. Whisk briskly about 30 strokes. Tap or shake any batter from whisk. Use rubber spatula to stir in hot water, scraping sides as necessary, just until batter is blended and smooth. With spatula scrape batter from bowl into prepared pan and spread to make a thin even layer.
Bake 14 to 16 minutes or until a wooden pick inserted into center comes out clean. Cool in pan on wire rack 10 minutes. Slide a thin metal spatula or knife around cake edges to loosen from pan. Invert cake onto rack. Remove paper liner; carefully turn cake right side up. Cool completely.
Cut cake crosswise in three equal rectangles. Thickly spread frosting on one piece, top with a second piece and spread with frosting. Leave top unfrosted. Thickly frost long sides. Before serving, dust top with cocoa powder. Makes 12 servings.
Easy Fudge Frosting
In medium saucepan melt butter. Stir in sugar, cocoa powder, and salt. Gradually stir in whipping cream. Heat, stirring constantly, until smooth and hot but not boiling. Remove from heat; stir in vanilla extract. Set aside; cool until thickened and spreadable. To cool quickly, loosely cover and refrigerate 1 hour. Store up to 1 week in refrigerator. Makes 2 cups.