Preheat oven to 180°C (350°F). Grease and line a 4-inch round cake pan. Whisk together the flour, cocoa powder, sugar, baking powder, and salt in a bowl.

Whisk the egg, milk, oil, and vanilla in a measuring cup. Pour into the dry ingredients and stir just until no flour streaks show. Do not overmix.

Scrape the batter into the pan, smooth the top, and bake 20 to 22 minutes until a toothpick comes out clean. Cool in the pan 10 minutes, then turn out onto a rack to cool completely.

For the frosting, beat 50 g softened butter with 25 g cocoa powder and 80 g powdered sugar until thick. Add milk a teaspoon at a time until spreadable. Frost the cooled cake and finish with chocolate shavings.