In a medium bowl, combine flour, soda, and salt. Mix well with a wire whisk set aside.
In a large bowl, blend sugars, using an electric mixer set at medium speed. Add butter, and mix to form a grainy paste, scraping the sides of the bowl. Add eggs, peanut butter and vanilla and mix at medium speed until light and fluffy.
Add the flour mixture and mix at low speed until just mixed.
Drop by rounded spoonfuls onto an ungreased cookie sheet. With a wet fork gently press cookies in a crisscrossed pattern. Bake for 18-22 minutes or until slightly brown along edges.
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