Preheat oven to 350 degrees F.
In the bowl of a standing mixer, add the room temperature butter, peanut butter, and brown sugar. Using the paddle attachment, cream until light and fluffy, or about 3 minutes.
Add the egg, slowly mix to combine, then add the vanilla, salt, and milk. and mix on low speed to combine.
In a separate bowl, whisk together the flour and baking soda, then add this to the butter mixture and mix on low, just until combined. Scrape down the sides of the bowl as needed to be sure there are no lumps of butter in your dough.
Once mixed, scoop and roll the cookie dough into 1¼" balls and place about 2" apart on a baking sheet lined with parchment paper or a silpat. Use a fork to flatten the cookies, creating a cross pattern.
Bake in your preheated oven for 7-8 minutes, or until the bottoms are very lightly browned.
Remove from the oven and let the cookies cool for 2 minutes on the baking sheet before transferring them to a cooling rack. Enjoy!