Adjust oven rack to middle position. Preheat oven to 350 degrees
Sift flour into bowl of a food processor (scoop and sweep method if not using a scale)
Add peanuts and pulse until fine (approximately 1 minute) almost like flour
Combine peanut butter, butter, sugar, salt, baking soda, baking powder and vanilla* in bowl of a stand mixer fitted with paddle attachment. I'm lazy, I add the vanilla to the milk and add it later.
Mix on low speed to moisten then increase to medium and beat until soft and light ab out 3 minutes
With mixer running add the egg in 2 additions, mixing untile ach is incorporated
Reduce speed to low and add peanut flour, followed by milk, mixing to form a very soft dough
Divide into 34-2 T (1.125 ounce) portions
Arrange on parchment lined baking sheet, 2 inches apart
Bake until the edges are firm and just beginning to brown but cookies are still puffy and steamy in the middle about 16 minutes
Cool on baking sheet until cookie is set about 10 minutes
Store in airtight container for up to 1 week at room temperature.