Add the stick of butter to a small saucepan over medium heat.
Stir the melted butter frequently for 5-10 minutes or until the butter starts turning brown.
As soon as the butter starts to turn color, remove from the heat and pour into a bowl. Refrigerate for at least an hour before making the frosting.
Add the cooled browned butter (and all the brown particles the sunk to the bottom!) and cream cheese to a mixing bowl. Beat until smooth.
Beat in the vanilla, 3 cups of the powdered sugar and the milk.
Add the additional cup of powdered sugar if it needs to be thickened a bit.
Spread on top of the cooled pumpkin bars.