Preheat oven: Preheat the oven to 350°F. Grease a 10x15-inch sheet cake pan or spray it with cooking spray.
Prepare the chocolate mixture: Add the butter, water and 4 tbsp of the cocoa powder to a medium saucepan over medium heat. Bring the mixture to a boil, stirring occasionally and cook until all the butter has melted. Remove from heat.
Mix the ingredients: In a separate large bowl combine the flour, sugar, baking soda and salt together. In another smaller bowl whisk together the sour cream, eggs and vanilla extract. Add the sour cream mixture to the flour bowl and whisk until combined.
Combine wet and dry mixtures: Pour the chocolate mixture from the sauce pan over the batter and mix with a hand mixer until the batter is smooth and there are no lumps.
Bake the cake: Pour the cake batter in the prepared sheet cake pan and transfer to the oven. Bake for 15 to 20 minutes or until set.
Prepare the frosting: About half way through baking the cake, add the milk and cocoa powder to a saucepan over medium-low heat. Cook until the butter has melted and mixture comes to a boil. Remove from heat and mix in the powder sugar using a hand held mixer. Mix until smooth and there are no more lumps.
Finish the cake: Pour the hot chocolate frosting over the hot cake and use a spatula to spread it evenly over the cake. Allow the frosting to set at room temperature for about 10 minutes before slicing the cake and serving.