Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan or an 18x13 inch half sheet pan.
In a large bowl, whisk together the flour, sugar, salt, and baking soda. Set aside.
In a medium saucepan, combine 0.5 cup butter, vegetable oil, 0.25 cup cocoa powder, and water. Bring to a boil, then remove from heat.
Pour the hot chocolate mixture over the dry ingredients and stir until just combined.
Whisk in the buttermilk, eggs, and 1 teaspoon of vanilla extract until the batter is smooth.
Pour the batter into the prepared pan and bake for 20 minutes, or until a toothpick inserted in the center comes out clean.
While the cake is baking, prepare the frosting. In a saucepan, melt 0.5 cup butter, 0.25 cup cocoa powder, and milk over medium heat until it begins to boil.
Remove from heat and whisk in the powdered sugar and 1 teaspoon of vanilla extract until smooth.
Pour the warm frosting over the hot cake as soon as it comes out of the oven. Spread evenly and let it cool before slicing.
Notes
Store any leftover cake in an airtight container at room temperature for up to 3 days.