Preheat the oven to 180 C / Gas 4. Grease a 15x20cm cake tin and line with baking parchment.
Melt the chocolate in a double boiler or in a pan over barely simmering water, stirring constantly.
In a mixing bowl beat the butter and sugar together until light and fluffy. Stir in the melted chocolate and vanilla extract then beat in the eggs, one at a time, until well incorporated. Slowly add in the flour while stirring then finally stir through the marshmallows. Transfer the brownie mixture to the prepared baking tin.
Bake in the preheated oven to 15 to 20 minutes until a skewer inserted into the centre comes out clean. Remove from the oven and allow to cool before slicing into squares or cut into squares and serve warm.