In large mixer bowl, dissolve yeast in warm water. Add milk, sugar, salt, cinnamon, nutmeg, eggs, shortening, and 2 cups flour. Blend for 30 seconds on low speed, scraping sides of bowl constantly. Beat 2 minutes on medium speed, scraping bowl occasionally. Stir in remaining flour until smooth. Cover and let rise in a warm place until double (50 to 60 minutes)
Turn dough onto a well-floured cloth-covered board; roll around lightly to coat with flour. (Dough will be soft to handle). With a floured stockinet-covered rolling pin, gently roll dough about ½ inch thick. cut with 2½ inch doughnut cutter.
Lift doughnuts carefully with a spatula (*I just used my fingers, the spatula messed mine all up) and place 2 inches apart on a greased baking sheet. Brush with melted butter. Cover; let rise until double, about 20 minutes.
Heat oven to 425 degrees. Bake 8-10 minutes or until golden in color. Watch carefully, they burn fast! Immediately brush doughnuts with melted butter and shake in sugar or cinnamon sugar.
Yield: Makes 1½ to 2 dozen.