In a large bowl, cream shortening and sugar until light and fluffy. Add eggs, one at a time, beating well after each addition. Combine flour, baking powder, nutmeg and salt; gradually add to creamed mixture alternately with milk, beating well after each addition.
Fill greased muffin cups two-thirds full. Bake at 350° for 18 minutes or until a toothpick inserted in the center comes out clean. Cool for 5 minutes before removing from pan to a wire rack. Dip doughnuts in melted butter, then roll in cinnamon-sugar. Serve warm.