Preheat the oven to 350°F (175°C) and grease a 9‑inch round cake pan.
In a large bowl whisk together flour, cocoa powder, sugar, baking powder, baking soda, and salt.
In another bowl combine melted butter, eggs, milk, and vanilla; mix until smooth.
Pour the wet ingredients into the dry mixture and stir just until combined; avoid over‑mixing.
Transfer batter to the prepared pan, smoothing the top with a spatula.
Bake for 7 minutes, then check for a springy surface; the center should be set but still moist.
Allow the cake to cool in the pan for 5 minutes before turning onto a wire rack to cool completely.