The Preparation
Preheat oven to 350 degrees F. Line baking sheets with parchment paper.
MAKE THE COOKIES: In a medium bowl, whisk together flour, baking soda, baking powder, and salt until well distributed.
In a stand mixer, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy (color should lighten).
Add the vanilla extract and egg to the butter-sugar mixture. Beat until combined.
Add the dry ingredients to the wet ingredients a little at a time on low speed until just combined.
Fold in 1 cup of quick oats by hand.
Using a small cookie scoop (the largest number/smallest size), portion dough onto prepared baking sheets.
Poke a hole in the center of each cookie with a skewer or toothpick (this prevents puffing and creates the classic Do-Si-Do look).
Bake for 10-15 minutes until golden brown on the bottom. Check at 10 minutes - they may need up to 15 depending on your oven. They will continue to set as they cool.
Remove from baking sheet and cool completely on a wire rack.
MAKE THE FILLING: In a stand mixer, combine softened butter and vanilla. Beat until smooth.
Add peanut butter and mix to combine.
Add powdered sugar gradually on low speed to avoid a cloud of sugar.
Add heavy cream and salt. Beat until smooth and spreadable. If too stiff, add a little more cream.
ASSEMBLE: Transfer filling to a piping bag. Pipe filling onto the flat side of one cookie, then sandwich with another cookie.
Makes about 10-12 sandwich cookies.