Preheat oven to 180 degrees C. Grease a 20x20cm baking pan.
Brownie: In a medium bowl, cream together butter and brown sugar until smooth. Beat in the egg and vanilla. Combine the flour, baking powder and salt; stir into the sugar mixture. Mix in the walnuts. Spread evenly into the prepared pan.
Bake for 25 to 30 minutes in the preheated oven, until the brownies start to pull away from the sides of the pan. Cool completely before icing.
Icing: Combine butter, brown sugar and milk in a small saucepan over medium- high heat. Bring to a boil and simmer for 2 minutes. Remove from heat, cool and beat in the icing sugar. Adjust the milk or icing sugar if necessary to achieve a good spreading consistency. Spread over cooled bars and let set before cutting into squares.