1Heat oven to 375°F. In medium bowl, stir cookie ingredients until soft dough forms.
2On floured surface, roll dough 1/8 inch thick. Cut with 2- to 2 1/2-inch round cookie cutter. Reroll and cut remaining dough. On ungreased cookie sheets, place cutouts 1 inch apart.
3Bake 7 to 9 minutes or until edges are set. Cool 1 minute; remove from cookie sheets. Cool completely, about 15 minutes.
4In small bowl, stir 2 tablespoons of the milk, the rum and powdered sugar until smooth. Add additional milk 1 teaspoon at a time to desired consistency. Drizzle over cookies. Let stand until glaze is almost set; sprinkle with coarse sugar.