Preheat oven to 350 degrees F.
In a large bowl, sift together flour, 1/3 cup cocoa powder, baking powder, and salt, and set aside.
In a medium bowl, whisk together eggs, granulated sugar, milk, butter, and vanilla; add to flour mixture. Stir batter until just combined. Spread batter evenly into an 8-cup shallow baking dish. Set aside.
In a medium bowl, whisk together remaining 1/3 cup cocoa powder, brown sugar, and boiling water. Pour evenly over batter. Bake until a cake tester inserted into the center of the cake comes out with crumbs adhering to it, 30 to 35 minutes. Let cool 10 minutes; serve warm with whipped cream.
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