First, preheat the oven to 325 F. Then, line a cookie sheet with parchment paper and grease with butter or cooking spray.
In a large bowl, using an electric mixer or a strong whisking arm, cream together the room temp butter and white and brown sugar until lighter and fluffy. Add in the eggs and vanilla and continue to beat until smooth and creamy. Add in the peanut butter and beat again until smooth. Then add in the flour, starch, salt, and baking soda and stir together with a spoon or spatula until fully combined. Dump in the chopped peanuts and quick oats and stir in until combined.
Then, spoon out tablespoons of the dough and roll into 1-inch balls. Place about 2 inches apart on the prepared cookie sheet and then press each ball down with a fork in a cross-hatch pattern (if you are filling the sandwiches, making the cookies flatter will make them easier to eat!). Bake for 10-12 minutes or until the edges are just starting to turn golden - they will not have that much color to them, that's what you want! Let cool completely before filling them.
Make the filling! In another large bowl, with the same electric mixer, beat together the room temp butter, peanut butter, and vanilla until smooth. Add in the powdered sugar, ½ cup at a time, until fully blended and stiffer. Add a pinch of salt and beat together - taste as you go!
Once cookies are cool, spoon on about a teaspoon of filling (or pipe on using a frosting piping bag), onto one cookie underside and pair it with an unfilled cookie. Complete with all cookies and then eat! (if you haven’t snuck one already!). I recommend letting these sit at room temp for about an hour to let the buttercream set a bit before biting into them (less messy) but they're ready to eat immediately if you're hungry.