Preheat your oven to 350°F (175°C). Grease a baking sheet.
In a mixing bowl, combine flour and sugar.
In a saucepan, melt butter. Add cocoa powder and boiling water. Bring to a boil, then remove from heat.
Pour the cocoa mixture over the flour mixture and stir until combined.
Add buttermilk, beaten eggs, baking soda, and vanilla extract. Mix well.
Pour the batter into the prepared baking sheet and bake for 20 minutes.
While the cake is baking, prepare the frosting. Melt butter in a saucepan. Add cocoa powder and milk, and bring to a boil. Remove from heat.
Stir in powdered sugar and vanilla extract until smooth.
Pour the frosting over the warm cake and spread evenly.
Let the cake cool before serving.