Using 1/2 teaspoon shortening for each cup, grease the bottom and sides of six cups of a popover pan. (Or, use six 6-ounce custard cups. Place greased custard cups in a 15x10x1-inch baking pan.) Set aside.
In a mixing bowl combine eggs, milk, and oil. Add flour. Beat with a rotary beater or wire whisk until mixture is smooth. Stir in dillweed or basil. Fill the prepared cups half full. Bake in a 400 degree F oven about 40 minutes or until very firm.
Immediately remove popovers from the oven and prick each with a fork to let steam escape. (If crisper popovers are desired, after baking, prick the popovers, turn the oven off, and leave popovers in the oven for 5 to 10 minutes more or until of desired crispness.) Serve hot. Makes 6.