Add butter and milk to a microwave safe bowl. Heat on HIGH for 1 minute and 30 seconds. Ensure the butter has melted fully. If not, heat for an additional 15 seconds.
Combine flour, brown sugar, cocoa powder and baking powder in a mixing bowl. Lightly whisk to combine. Add chocolate, walnuts and vanilla extract. To this, add the butter and milk mix while it is hot. Fold well until all the ingredients are combined and the chocolate has melted. It is alright if there still a few chunks of chocolate, it will melt while baking.
Transfer the mixture into an 8 inch round microwave safe dish. Use a spatula to level it.
Combine all the ingredients mentioned under sauce and whisk until there are no lumps. Pour it into the pudding dish over the cake batter.
Microwave on MEDIUM (50%) for 11 minutes or until a skewer inserted into the edge comes out clean.
Serve with vanilla ice cream and dust some additional icing sugar or cocoa powder on top.