Preheat oven to 350. In a bowl 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.