Sift flour, nutmeg and salt together; set aside.
Cream butter; add sugar and cream until fluffy. Add extracts and mix well. Add egg.
Gradually mix in dry ingredients very well. Chill dough 30 minutes or overnight.
Line baking sheets with brown paper. Shape dough by tablespoonsful into balls and place on papered sheets about 1-1/2 inches apart. Bake 10 to 12 minutes, do not brown.
Remove from pans and cool on racks. Ice.
Icing: Cream butter; add extracts and mix. Add powdered sugar gradually; mix well. Stir in enough milk to make spreadable but not runny. Top with half of a glaceed cherry.
Recipe submitted by ~Donna~ V on 12/10/99