Preheat oven to 350°F and grease a 9x13-inch baking pan.
Whisk flour, sugar, baking soda, and salt in a large bowl.
Melt butter with water and cocoa powder in a saucepan over medium heat, then pour over flour mixture and stir to combine.
Mix in eggs, sour cream, and vanilla until smooth, then pour into prepared pan and bake 25-28 minutes.
While cake is finishing, melt frosting butter with cocoa powder and milk, then whisk in powdered sugar until smooth.
Pour warm frosting over hot cake and spread evenly, then let set before slicing.