Mix together brown sugar, 1/2 cup butter or margarine, egg, buttermilk and 1 teaspoon of root beer extract.
Add flour, baking soda and salt and mix well.
Drop teaspoon sized pieces of dough 2 inches apart on greased cookie sheets. Bake for 6 to 8 minutes.
To Make Root Beer Glaze: Mix together confectioner's sugar, 1/3 cup butter or margarine, 1 1/2 teaspoons of root beer extract and hot water. Brush on top of hot cookies.
