Heat oven to 375F. Then in a medium bowl stir cookie ingredients until soft dough forms. Then on a floured surface roll dough 1/8 inch thick. Cut with 2 to 2 1/2 inch round cookie cutter. Reroll & cut remaining dough. On ungreased cookie sheets place cutouts 1 inch apart.
Then bake for about 7 to 9 mins or until edges are set. Cool 1 min & remove from cookie sheets. Cool completely about 15 mins.
Then an a small bowl stir 2 tablespoons of the milk the rum & powdered sugar until smooth. Then add the additional milk 1 teaspoon at a time to desired consistency. Then drizzle over cookies & let stand until glaze is almost se. Then sprinkle with coarse sugar.