Preheat the oven to 350 degrees. Spray a 9x13 pan with nonstick spray and set aside.
Add the brown sugar, white sugar, flour, cocoa powder, baking soda, baking powder and salt to a large mixing bowl and combine.
In another bowl add the eggs, milk, oil, and vanilla extract and whisk together.
Add the wet ingredients to the dry ingredients and beat together until well combined. Scrape down the sides as needed.
Slowly pour the hot water into the batter and mix on low speed until well combined. Continue to scrape down the sides and bottom of the bowl as needed to make sure everything is mixed well. The batter will be very thin.
Pour the batter into the prepared 9x13 pan and place in the preheated oven. Bake for 25-35 minutes until a toothpick can be inserted and comes out with a few moist crumbs.
Remove the cake from the oven and allow to cool completely.