Preheat the oven to 170°C and grease a 7-inch cake pan. Lightly grease with butter and dust it with flour to prevent sticking.
In a mixing bowl, whisk together the flour, cocoa powder, baking powder, baking soda, salt, brown sugar, and granulated sugar.
Add the egg, buttermilk, vanilla, and oil, then whisk until you have a smooth batter.
Pour in the hot water and mix again until fully incorporated. The batter will be quite thin-this is normal.
Transfer the batter to the prepared pan and bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool completely, then slice it horizontally into two even layers.