In a bowl, whisk together flour, baking soda, and baking powder. Set aside.
In the large bowl of a stand mixer, beat together the butter, peanut butter, and both sugars until the mixture is light and fluffy, about 2 minutes on medium-high. At medium-low speed, add eggs one at a time and vanilla, mixing until well incorporated. At low speed, slowly mix in the dry flour mixture. When dough is combined, wrap tightly in cling wrap, and place in fridge to chill for at least an hour.
Preheat oven to 375F. To make peanut shape, form cookie dough into 1 inch balls and flatten into a long oval shape (1" x 2") about 2 inches apart. Use a fork to make criss cross pattern, and pinch center gently to create peanut shape. Keep rest of dough cold while you make one batch at a time. (To make round cookies, flatten 1 inch dough balls into circles about 1/2 inch thick, and use a fork to press pattern on them.)
Bake 8-9 minutes, or until edges are lightly browned. Pinch cookie centers again, if needed, to keep peanut shape. Sprinkle hot cookies with granulated sugar. Cool a few minutes on baking sheet and finish cooling on wire rack. Once cookies are completely cooled, they can be filled.
To make the filling, beat together the butter and peanut butter in a large bowl until smooth and fluffy. Gradually add in powdered sugar and beat until filling is smooth. Add 1 TB milk at a time, until desired consistency. Fill to your heart's content!