Preheat oven to 350º. Line cookie sheets with parchment paper.
In a bowl, add the flour, salt, and baking soda and whisk together. In a separate bowl, whisk together the eggs and vanilla.
In the bowl of an electric mixer, cream together the peanut butter, butter and sugars on medium speed for 2 minutes, until well combined, scraping the sides. Gradually add the egg mixture until well combined.
With the mixer on low speed, add the dry ingredients in stages. Mix only until everything is just combined, scraping down sides and bottom. Add the salted peanuts and continue mixing on low speed until the nuts are evnely distributed.
Using an ice cream scoop, scoop out 1/8 cup balls and place on prepared cookie sheet. Flatten each ball by pressing the top down firmly with the flat of your hand, then use the tines of a fork to make a criss-cross pattern in the center.
Bake for 10-12 minutes until they are golden brown and just set. Cool on baking sheet for 5 minutes, then transfer to wire rack to cool completely.