Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13 inch baking dish.
In a large bowl, cream together the butter, brown sugar, and white sugar until smooth. Beat in the eggs one at a time, then stir in the vanilla. Combine the flour, baking powder, and salt; stir into the batter just until blended. Fold in the shredded yam. Spread the batter evenly in the greased baking dish.
Bake for 30 minutes in the preheated oven, until a toothpick inserted into the center, comes out clean. Mix together the confectioners' sugar, butter and milk until smooth. Spread over the brownies while they are still warm. They will absorb some of the glaze. Serve hot or warm.