In a medium saucepan, heat butter and brown sugar over medium heat until bubbly. Cook, stirring constantly, for one minute or until slightly thickened.
Beat in the milk. Blend in confectioner's sugar until the glaze is smooth and spreadable.
Use a spoon to drizzle icing over top of cookies.
I've made this with whole wheat flour too, in the same ratios, and no one can taste the difference!
If the glaze hardens or gets a shell, put it back on the burner over low heat and stir until it's spreadable again.
Adapted from Genius Kitchen