Preheat the oven to 375 degrees F/190 degrees C. Line a baking sheet with parchment paper.
In a medium bowl, combine the flour, baking soda, and salt. Set aside.
In a stand mixer bowl, or a separate large bowl if using a hand mixer, add the butter, peanut butter, vanilla, sugar, and milk. Beat together on medium speed.
Lower the speed, add the flour mixture to the bowl, about a quarter at a time until it has all been combined and a dough is formed.
Roll the dough into small balls, about 1 1/2 - 2 tablespoons each, and line up on the baking sheet. Flatten each of the dough balls gently with the palm of your hand.
Use a fork to press down on the cookies twice, perpendicular to make a checkered pattern.
Bake for 11-13 minutes. Let cool for 5 minutes, then transfer to a cooling rack and let cool completely. Enoy & share!