Preheat an oven to 350F. Line 2 large cookie sheets with parchment paper.

In a medium bowl, whisk together the oats, flour, baking powder, baking soda, and salt. Set aside. In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and both sugars until light and fluffy. Add egg, Skippy creamy peanut butter, and vanilla. Pour oat mixture into peanut butter mixture, mixing until just combined.

Place rounded teaspoonfuls of batter on the baking sheets, leaving about 2 inches between each one. Pat dough down so they form small flattened circles. Bake for about 8 minutes or until golden. Let cool on a wire rack.

While the cookies are baking, beat the butter, powdered sugar, and Skippy peanut butter until combined. Add milk as needed to achieve desired consistency.

To make cookie sandwich, spread a bit of frosting on one cookie, top with another cookie.