In a bowl, stir together flour, cornmeal, sugar, baking powder, dry mustard, and salt. Cut in shortening until mixture resembles fine crumbs.
In a bowl, mix together egg and milk. Add to flour mixture and mix well.
Insert wooden skewers into the ends of frankfurters. Pour cooking oil into skillet to a depth of 1 inch; heat oil to 365 degree F.
Coat franks with batter. (If batter is too thick, add 1 to 2 tablespoons milk.) Place coated franks, 3 at a time, in hot oil. Turn franks with tongs after 10 seconds to prevent batter from sliding off. Cook for 2 to 3 minutes more or until golden, turning again halfway through cooking time.
Serve hot with catsup and mustard, if you like. Makes 8 to 10 servings.