Cream butter; add sugars gradually, beating until creamy. Mix in egg, peanut butter, salt and baking soda. Blend in flour, slowly. Add vanilla and mix well. Roll into small balls (or drop by teaspoonfuls) and place on a greased cookie sheet. Press the balls flat with a floured fork. Bake in a moderate oven 350° F 10 to 12 minutes. Yield: 4 1/2 to 5 dozen. Note: I know every cookbook tells you not to double a recipe, but this one can be. I always double it and freeze 4 dozen. They freeze very well.