Sift together the flour, salt, and baking powder and set aside. Cream butter or shortening and sugars, add the eggs and vanilla. Add the dry ingredients and the peanut butter. Mix well and knead.
Roll into 3/4-inch balls and place on greased cookie sheets, 1 inch apart. Flatten criss-cross style with a fork dipped in flour. Brush with egg white and sprinkle with chopped nuts if desired. Bake for 10 to 12 minutes.