In large bowl, beat sugar and 1 cup butter with mixer on medium speed until fluffy. Beat in vanilla, 2 tsp rum flavor and the egg until smooth. Beat in flour and 1 tsp nutmeg.
Place 1/4 of the dough at a time in cookie press.
On ungreased cookie sheet, form desired shapes with dough.
Bake 6-10 minutes until edges are lightly browned. Cool 1 minute; form desired shapes with dough.
In small bowl, stir all glaze ingredients except nutmeg with spoon until smooth and thin enough to drizzle. Pour mixture into small resealable plastic food-storage bag; cut off tiny corner of bag. Squeeze bag to drizzle glaze on cookies. Before glaze is set, sprinkle 1/2 tsp nutmeg over cookies.