Preheat the oven to 375 degrees F (190 degrees C). Sift together flour, baking soda, and salt; set aside.
In a medium bowl, cream together butter, peanut butter, 1/2 cup white sugar, and brown sugar until smooth. Beat in egg, then stir in vanilla. Gradually blend in the sifted ingredients. Shape dough into 1 inch balls. Roll in remaining sugar. Place 2 inches apart on ungreased cookie sheets. Criss-cross with fork tines.
Bake at for 10 to 12 minutes in the preheated oven. Cool slightly, and remove from pan.
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