In a mixing bowl for a stand mixer, combine butter, peanut butter, white sugar, and brown sugar until light & fluffy, about 2 minutes on medium speed.
Add in eggs, vanilla, baking soda, and baking powder. Mix until well combined making sure to scrape down sides during mixing.
Add flour in 1/2 cup at a time mixing on low speed until all combined.
Cover with cling wrap and refrigerate for 1 hour.
Preheat oven at 375 degrees and line baking pan with parchment paper. Using a 1' cookie scoop form dough into 1' inch balls and flatten into log shape rolls. Roll into 1/3 cup white sugar. Place onto baking pan 1-2 inches a part from each other to allow room to spread while cooking.
Take a fork and place on log shaped cookie dough and mash down to form the lines. Then take fork and place it on the short end of log shaped cookie dough and mash down to form lines crossed over the first line.
To give the cookie the classic peanut shape, pinch the middle of the cookie a little bit with your fingers.
Place in oven and bake for 7-8 minutes until a nice golden brown color on the bottom of cookie. Place pan on a rack and cool for 2-3 minutes to help cookie form. Place cookies on the cooking rack to completely cool.
Making the filling-In clean bowl for stand mixer using a whisk attachment, mix together butter and peanut butter on medium speed until smooth.
Add in powdered sugar 1 cup at a time until desired smoothness is met. (Mix slowly). If needed, add milk 1 TBS at a time to smooth out filling.
Spread filling onto bottom of one cookie then place the bottom of another cookie on the filling to create the sandwich cookie. Enjoy.
