Preheat the oven to 375 degrees. Sift the flour, soda, and salt together, and set aside. Work the shortening and butter together, with a spoon, until fluffy and creamy. Add the sugar slowly, continuing to work until light. Then add the egg yolk and beat until light and fluffy. Add the flour mixture alternately with the buttermilk, beating well after each addition. Stir in the vanilla and then gently fold in the stiffly beaten egg white.
Drop by rounded tablespoonfuls 3 inches apart on a greased cookie sheet. Flatten with a spatula to 1/2-inch thickness. Bake in the preheated over for 20 minutes or until done.
Makes 18 cookies.