Sift together the flour, and baking soda, set aside. In a medium bowl, cream the white sugar and brown sugar with the butter. Stir in the eggs, one at a time, then the vanilla and peanut butter. Add the dry ingredients to the creamed mixture and stir until combined. Finally, stir in the nuts.
Drop by heaping teaspoonfuls onto cookie sheets. Bake for 12 to 15 minutes in the preheated oven. Cool on wire racks.
