1Heat oven to 350°F (if using dark or nonstick cookie sheet, heat oven to 325°F). In large bowl, beat granulated sugar and 1 cup butter with electric mixer on medium speed until fluffy. Beat in vanilla, 2 teaspoons rum extract and the egg until smooth. Beat in flour and 1 teaspoon nutmeg.
2Place 1/4 of the dough at a time in cookie press. On ungreased cookie sheet, form desired shapes with dough.
3Bake 6 to 10 minutes until edges are lightly browned. Cool 1 minute; remove from cookie sheet to cooling rack.
4In small bowl, stir all glaze ingredients except nutmeg with spoon until smooth and thin enough to drizzle. Pour mixture into small resealable food-storage plastic bag; cut off tiny corner of bag. Squeeze bag to drizzle glaze on cookies. Before glaze is set, sprinkle 1/2 teaspoon nutmeg over cookies.