Into a bowl, sift together flour, baking soda, nutmeg, and salt. Cream shortening; gradually add sugar, beating until light and fluffy. Add egg; beat well. Stir in vanilla.
Add combined vinegar and milk alternately with dry ingredients; stir just until well blended.
Roll small quantities of the dough at a time, to about 1/3-inch thick. Cut doughnuts with a 2 1/2-inch cutter and let stand for about 10 minutes. Fry in hot fat at about 365° to a nice golden brown. Turn once. Fry only 3 or 4 batches at a time to keep fat from cooling down. Drain on paper towels. Makes about 18 doughnuts.
Calories per serving: 190