Melt the butter and sugar together in a saucepan over low heat. Add the milk, then remove from heat. Stir in the chocolate until melted and smooth. Let it cool.
Sift the flour and cocoa powder into a large bowl.
Pour the melted mixture into the dry ingredients and mix until just combined.
Spread the batter into the prepared pan and bake for about 20 minutes, or until the top is set.