In a large bowl, beat brown sugar and 1 cup butter until light and fluffy. Add egg yolk and blend well. Stir in flour; mix well. Cover with plastic wrap; refrigerate 15 minutes for easier handling.
Heat oven to 325 degrees F. Shape dough into 1 inch balls. Place 2 inches apart on an ungreased cookie sheet. Flatten to 1 1/2 inch circles with a fork dipped in flour. Bake at 325 degrees F. for 10 to 14 minutes or until cookies are a light golden brown. Immediately remove from cookie sheets and cool completely.
Heat 2 tablespoons butter in a medium saucepan over medium heat until light golden brown. Remove from heat. Stir in remaining frosting ingredients, adding enough milk for desired spreading consistency. Blend until smooth. Spread 1 teaspoon frosting between 2 cooled cookies. Repeat with remaining frosting and cookies.
Add addition milk to frosting if it stiffens as it cools so spreading consistency is desirable.
