Mix shortening, butter or margarine, sugars, eggs and vanilla thoroughly. Stir in all purpose or unbleached flour, baking soda and salt. Turn dough onto lightly floured board. Shape dough into ball with lightly floured hands, pressing to make dough compact. Cut dough in half. Shape each half into a roll 2 inches in diameter and about 8 inches long by gently rolling dough back and forth on floured board. Roll dough onto plastic wrap: wrap and twist ends tightly. Dough can be refrigerated up to 1 month or frozen up to 3 months. Preheat oven to 375 degrees F (190 degrees C). Cut roll into 1/4-inch slices. (It is not necessary to thaw frozen dough before slicing.) Place slices about 2 inches apart on ungreased baking sheet. Bake 9 to 11 minutes. Immediately remove cookies from baking sheet onto wire rack.
Variations: CHOCOLATE CHIP: Add 1 cup mini semisweet chocolate chips and 1 cup chopped nuts with the flour. OATMEAL-COCONUT: Reduce flour to 2 3/4 cups. Add 1 cup flaked coconut and 1 cup quick-cooking oats with the flour. PEANUT BUTTER: Add 1 cup creamy or chunky peanut butter with the shortening. CHOCOLATE-NUT: Add 1 cup chopped nuts and 1/2 cup cocoa with the flour. FRUIT SLICES: Add 1 cup whole candied cherries, 1/2 cup chopped nuts and 1/2 cup cut-up mixed candied fruit with the flour.