Preheat oven to 350°F.
Start with the cookies. In a medium bowl, whisk together the flour, baking powder, baking soda and salt.
In a large bowl, cream together butter and peanut butter. Beat in the sugars until fluffy, then add in the eggs one at a time, waiting until each is fully incorporated before adding the next. Stir in vanilla extract.
Working at a low speed, mix in the flour, followed by the oats (if you don’t have quick-cooking, pulse whole rolled oats in the food processor to chop them up a bit).
On a parchment-lined baking sheet, drop teaspoonfuls of batter (roughly 3/4-in. sized balls), leaving about 2 inches between each to allow for spread.
Bake for about 10 minutes, until cookies are a light golden brown. Cool on baking sheet for 5 minutes, making small holes in 1/2 of the cookies (for the tops of the sandwiches) before they set up. Transfer to a wire rack to cool completely.
Once cookies have cooled, make the filling.
In a large bowl, cream together smooth peanut butter, butter and confectioners’ sugar until very smooth. Spread 2-3 tsp onto half of the finished cookies and sandwich with the remaining halves. If you chose to make yours with GS-lookalike holes in some of the cookies, use these as the tops of the sandwiches.
Store in an airtight container.
Note: Use unsalted butter with this recipe, as different brands of peanut butter can vary hugely in salt content and it’s possible you’ll end up with a too-salty cookie with the salted butter, salted peanut butter and added salt. If you must use salted butter and are using brand of peanut butter that seems a bit salty, you can always reduce or eliminate the added salt. Personally, I like the salty sweet combination with peanut butter, but it’s only fair for me to give a little warning just in case!