Preheat the oven to 350°F. Grease a half sheet pan (18in x 13in) with nonstick spray and set aside.
In a large bowl, whisk together the granulated sugar, flour, baking soda, and salt. Set aside.
2½ cups granulated sugar, 2½ cups all-purpose flour, 1¼ teaspoons baking soda, ¼ teaspoon salt
In a separate bowl, whisk together the eggs, buttermilk, and vanilla. Set aside.
3 large eggs, ⅔ cup buttermilk, 2 teaspoons vanilla extract
In a saucepan over medium heat, combine the water, butter, and cocoa powder. Bring to a boil, stirring occasionally.
1¼ cups water, 1⅓ cups salted butter, 3 Tbsp cocoa powder
Pour the hot cocoa powder mixture over the dry ingredients and mix until combined.
Whisk in the egg mixture until the batter is smooth.
Pour batter into the prepared pan and bake for 20 minutes, or until set.
While the cake is baking, add the milk, cocoa powder, butter, and vanilla to a saucepan. Bring to a gentle boil, stirring frequently.
¼ cup milk + more to thin, 3 Tbsp cocoa powder, 10 Tbsp butter, 2 teaspoons vanilla extract
Remove from heat and whisk in the powdered sugar until smooth. Whisk in more milk, a small amount at a time, to think the frosting to your liking.
3 1/2 cups powdered sugar
Pour the warm frosting evenly over the hot cake and spread to cover.
Let the cake cool completely before slicing and serving. Enjoy!