Preheat the oven to 350°F. Butter and dust your 9x13 pan with cocoa powder to prevent sticking.
In your saucepan, boil the butter, water, and cocoa powder. Cool completely.
Whisk together the flour, sugar, baking powder, and salt and create a well in the mixture.
Beat the eggs, vanilla, and sour cream together in the well. Then, gently fold into the flour mix. Then whisk in the cocoa liquid.
Pour your batter into the 9x13 pan, and bake for 20 to 25 minutes until a toothpick inserted in the center comes out clean.
When the cake has about 10 minutes left, melt the butter and milk for the frosting in your saucepan (don't clean it out). Whisk in the cocoa and powdered sugar until no lumps remain.
Pour the warm icing over your cake as soon as it comes out of the oven. Cool completely before serving.