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 in the egg, then mix on low to combine. Then add in the vanilla, salt and milk and mix on low 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 1 ¼" balls and place on a baking sheet lined with parchment paper or a silpat. Use a fork to flatten the cookies, creating a cross pattern.
Bake 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!