In the bowl of a large electric mixer, using the paddle attachment, whip the butter on high speed until very soft. Meanwhile, place a large sheet of parchment paper on a work surface. Using a large sifter, sift a pound of confectioners' sugar onto the parchment. This helps prevent clumping, and makes the mixing easier. Lower the speed of the mixer, and, using the parchment as a funnel, pour the sugar into the bowl and mix slowly until combined. Add the milk and mix until combined. Sift the second pound of sugar onto the parchment sheet. Again at low speed, add the sugar and mix well. Once combined, sift the remaining sugar and add it with the vanilla and mix. Once it is combined, turn the mixer speed up and beat the icing until very light and fluffy, about 3 to 4 minutes.
If desired, divide the icing into smaller batches and color with food coloring.
Spread the icing on cooled cupcakes while at room temperature. Refrigerate any leftover icing, but be sure to let it come back to room temperature before using. Re-whip the icing to make it fluffy again.