Preheat your oven to 325°F. Spray a 13x18-inch sheet pan (or jelly roll pan) with non-stick spray. This size gives the cake its signature thin, spread-out look.

In a large mixing bowl, whisk together the flour, sugars, baking soda, and salt. Set this mixture aside.

In a medium saucepan, melt the butter over medium heat. Once melted, add the water and cocoa powder. Stir until the mixture is smooth and begins to simmer. Remove the saucepan from the heat and let it cool slightly.

Pour the chocolate mixture into the bowl with the dry ingredients, stirring gently to combine. In a small bowl, whisk together the buttermilk, eggs, and vanilla extract, then add this mixture to the batter. Stir until everything is well-combined and smooth.

Pour the batter into your prepared sheet pan, spreading it evenly. Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs on it. The cake should be soft and moist, but not jiggly.

While the cake is baking, begin making the icing. In a medium saucepan, melt the butter over medium heat. Stir in the cocoa powder and milk, whisking until smooth. Remove from heat, then add the vanilla extract. Gradually whisk in the powdered sugar until the icing is smooth and thickened. You can adjust the amount of powdered sugar to achieve your preferred consistency.

Once the cake is out of the oven, allow it to cool for about 5 minutes. Pour the warm icing over the slightly warm cake, spreading it evenly with a spatula. The icing should seep into the cake, adding moisture and flavor to every bite.

Allow the cake and icing to cool completely before cutting into squares. As tempting as it may be to dive in right away, giving the cake time to set will help the flavors meld together.