Preheat your oven to 350°F (180°C) and get your 6-inch pan ready by lining it with baking paper and lightly greasing the sides, this little step makes sure your mini cake comes out perfectly every time.
In a medium bowl, whisk together the vegetable oil, brown sugar, granulated sugar, egg, extra yolk, and vanilla until smooth and glossy. Add the milk and mix again until silky, this is when the batter starts to feel dreamy and ready to bake.
In another bowl, combine the flour, Dutch-process cocoa, baking soda, baking powder, and salt. Give it a good whisk so all the dry ingredients are evenly mixed, this ensures a soft, tender cake with no clumps.
Pour the wet ingredients into the dry mix, then stir in the hot coffee. Gently fold everything together until smooth. Be careful not to overmix, you want a light, tender cake, not a dense one.
Pour the batter into the pan you’ve prepped, then smooth the surface until it’s uniform. Bake for 30–33 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs. Let the cake cool in the pan for about 10 minutes, then carefully move it to a wire rack.
While the cake cools, beat the butter until creamy. Mix in the cocoa, vanilla, and half of the powdered sugar on low speed to avoid a sugar cloud. Gradually add the rest of the powdered sugar and a splash of milk if needed, until the frosting is silky and spreadable.
Once your cake is completely cool, spread the frosting evenly on top. Then enjoy every indulgent, chocolatey bite.