Preheat the oven to 350°F.
In an ungreased 8×8-inch glass or ceramic baking dish, combine the flour, sugar, cocoa powder, salt, and baking soda. Stir until the dry ingredients are well blended.
Make three separate wells in the dry mixture. Pour vegetable oil in one, vanilla extract in another, and white vinegar in the last.
Pour the water evenly over everything, then stir the mixture until smooth using a whisk or fork.
Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool completely before adding the frosting.
In a small bowl, whisk together the powdered sugar and cocoa powder.
Slowly add the water, one tablespoon at a time, stirring continuously until the mixture reaches a smooth, thick, and pourable consistency.
Pour the frosting over the cooled cake and spread evenly. Allow it to set before slicing into squares.
