Heat oven to 375 and prepare cookie sheet(s) for use.
Mix flour and baking soda.
Beat butter and peanut butter in a large bowl with electric mixer until creamy. Add sugars and beat until fluffy. Beat in egg and vanilla until well blended. With mixer on low speed gradually add flour mixture. Beat just until blended.
Roll heaping teaspoonfuls of dough into balls. Place 1 1/2 inches apart on ungreased cookie sheet. Flatten with fork, making a crisscross design.
Bake 10 to 12 minutes until browned.
Cool on cookie sheet for 1 minute before removing to wire rack to cool completely.