Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch cake pan.
Whisk buttermilk, vegetable oil, eggs, 1/3 cup cocoa powder, and 1 teaspoon vanilla extract in a bowl until smooth.
Whisk flour, sugar, baking soda, and 1/2 teaspoon salt in a separate bowl.
Add dry ingredients to buttermilk mixture and whisk in hot water.
Spread batter in prepared cake pan.
Bake in the preheated oven until set and a toothpick inserted into the center of the cake comes out clean or with moist crumbs, about 35 minutes.
Let cool.
Beat confectioners' sugar, cream, butter, 1/4 cup cocoa powder, 1 teaspoon vanilla extract, and 1/4 teaspoon salt in a bowl using an electric mixer until frosting is smooth and creamy.