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To make cake:.
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Preheat oven to 350u00b0F with rack in middle. Butter and flour a 9-inch square cake pan (2 inches deep).
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Whisk together flour, cocoa powder, baking soda, and salt.
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Beat together butter and brown sugar with an electric mixer until pale and fluffy. Add eggs 1 at a time, beating well, then beat in vanilla.
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Add flour mixture and water alternately in batches, beginning and ending with flour mixture and mixing until just combined.
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Pour batter into cake pan and smooth top, then bake until a wooden pick inserted in center comes out clean, 45 to 55 minutes.
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Cool in pan on a rack 1 hour.
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Transfer cake to a cake plate.
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Make frosting:.
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Combine frosting ingredients with a pinch of salt in a metal bowl set over a saucepan of simmering water and beat with a handheld electric mixer at high speed until frosting is thick and fluffy, 6 to 7 minutes.
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Remove bowl from heat and continue to beat until slightly cooled.
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Mound frosting on top of cake.
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Dust with additional cocoa powder.
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Cooks' notes:.
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Cake, without frosting, will improve in flavor if made 1 day ahead. Cool, then keep, wrapped in plastic wrap, at room temperature. Frost cake just before serving.
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The egg whites in the frosting are not fully cooked. You can substitute pasteurized or reconstituted dried egg whites if salmonella is a problem in your area.
