Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan.
In a large bowl, whisk together 2½ cups of flour, 2 cups of sugar, ¾ cup of cocoa powder, 2 teaspoons of baking soda, 1 teaspoon of baking powder, and ½ teaspoon of salt.
Add 3 eggs, 1¼ cups of milk, ¾ cup of oil, and 2 teaspoons of vanilla extract. Whisk until smooth.
Slowly pour in 1¼ cups of hot coffee, whisking constantly. The batter will be very thin, that’s exactly what you want.
Pour the batter into the prepared pan. Bake for 35 to 40 minutes, until a toothpick inserted in the center comes out clean.
While the cake bakes, add ½ cup of butter, 6 tablespoons of milk, and 4 tablespoons of cocoa powder to a saucepan over medium heat. Stir until the butter is melted and the mixture is smooth. Do not let it boil.
Remove from heat and whisk in 3¾ cups of powdered sugar, 1 teaspoon of vanilla, and ¼ teaspoon of salt until smooth.
Pour the warm frosting over the warm cake and spread evenly. Let it set for about 15 minutes before slicing.