Preheat the oven to 350º. Grease an flour a 15X10x1 inch baking pan; set aside. (It will not work in a regular cookie sheet. It needs the one inch sides.)
To make the cake: In a large mixing bowl, combine the flour, granulated sugar, baking soda and salt; set aside.
In a medium saucepan, stir together the 1 cup butter, the
water and the 1/4 cup cocoa powder. Bring the mixture just to a boil, stirring constantly; remove from heat.
Add the cocoa mixture to the flour mixture. Beat with an
electric mixer on low speed until all of the ingredients are well blended. Add the eggs and sour cream. Beat on medium to high speed for 1 minute more.
Pour the batter into the prepared baking pan. Bake in the 350º oven about 25 minutes or until a wooden toothpick inserted near the center of the cake comes out clean; remove from oven.
Meanwhile, to make the frosting: In a medium saucepan, stir together the 1/2 c. butter, the milk and the 1/4 cup cocoa powder. Bring the mixture to a boil; remove from heat. Add the powdered sugar and vanilla. Beat with an electric mixer on medium speed until the frosting is smooth.
Pour the warm frosting over the warm sheet cake, spreading the frosting evenly. Let the cake cool in the pan on a wire rack.