In the bowl of an electric stand mixer fitted with the paddle attachment, cream together the butter, peanut butter and both sugars on medium-high speed until light and fluffy. Add the egg, egg yolk, and vanilla and continue beating until combined.

Stop the mixer and scrape down the sides of the bowl. Add the flour, baking soda, and salt, and mix on low speed until just incorporated, about 1 minute.

Using a small cookie scoop, or two spoons, form mounds about the size of golfballs and place them on the prepared baking sheet. Slightly flatten the mounds with your hand to allow them to bake more evenly.

Bake for 8 to 10 minutes, or until edges have set and tops look slightly underbaked, pale and glossy in the center. Allow cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

While cookies are cooling, prepare the buttercream. To the bowl of a stand mixer fitted with a paddle attachment, beat the butter on medium-high speed until light and fluffy, about 2 minutes.

Reduce the speed to low and add the powdered sugar, a half cup at a time, mixing well after each addition. Scrape down the sides of the bowl, as needed. Add the maple syrup and salt and beat on high until light and creamy, about 3-4 minutes. Transfer buttercream to a pastry bag fitted with desired tip*.

To assemble the cookies, pipe the frosting on one side of the cookie. Place a second cookie on top and gently press down.