Preheat oven to 350. Sift flour and baking soda into a bowl.
Put butter and both sugars in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy; about 3 minutes.
Add egg; mix until well combined. Mix in vanilla and then peanut butter.
Reduce speed to low. Add flour mixture; mix until just combined. Stir in peanuts.
Drop batter by heaping tablespoons onto baking sheets lines with parchment paper, spacing 1 1/2 inches apart.
Dip the bottom of a galss in flour, tapping off excess and use it to flatten balls slightly. Firmly press fork tines into each dough ball to make a cross-hatch pattern.
Bake cookies, rotating sheets halfway through, until centers are firm and edges are lightly browned, about 25 minutes. transfer cookies on parchment to a wire rack to cool completely. Cookies can be stored in airtight containers at room temperature up to 3 days.