To make glaze: Whisk confectioners' sugar, vanilla and enough of the milk to make a smooth, thick glaze. When the doughnuts are completely cool, set them, fluted-side up, on a wire rack over wax paper. Spoon some glaze over each doughnut, letting it drip down the sides. (Alternatively, dip the doughnuts in glaze.) Let stand until glaze has set.