Break the chocolate into small pieces then melt in a bowl set over a pan of nearly simmering water. Gently and constantly stir the chocolate while keeping the water just below simmering (don't let the bottom of the bowl rest on the bottom of the pan or it will get too hot and the chocolate will separate into liquid cocoa butter and clumps of cocoa powder). Once melted, add the butter and allow to melt, stirring into the chocolate.
Mix the cocoa powder with the flour and the sugar and, off the heat, mix this combination into the butter and chocolate. Beat the eggs and chop the marshmallows. Add the eggs and fold the marshmallows into the mixture. Line a 12" (30cm) square cake tin with baking parchment. Turn the brownie mixture into the tin and bake in a preheated moderate oven (Mk 5 - 375ºF - 190ºC) for about 20 minutes until the surface has set but still it feels soft and slightly squashy underneath.
Allow to cool and cut into squares. There is nothing like these Marshmallow Brownies with a glass of cold milk. Try them and I think you will agree they are the best brownies you have ever had.