Preheat the oven to 350ºF.
Beat the butter, peanut butter and sugars in the bowl of a stand mixer fitted with the paddle attachment until light and fluffy, about 3 minutes. Add the eggs, one at a time, then add the vanilla and baking powder.
Add the flour to the mixer one cup at a time, scraping down the sides of the bowl between each addition and beating just until combined.
Lightly flour your work surface then roll out the dough to 1/8-inch thick. Cut out as many 3-inch cookies with the circular cookie cutter as possible then use the smaller cookie cutter to cut out openings in the center of half of the cookies. (Scraps can be re-rolled.)
Transfer the cookies to parchment- or Silpat-lined baking sheets, spacing them 1 inch apart.
Bake the cookies for 10 to 12 minutes, or until golden brown and slightly crisp on edges. Remove and transfer to a cooling rack.
Once the cookies have fully cooled, spread about 1 tablespoon of jelly on the non-cutout cookies, and then place a cutout cookie on top to form sandwiches. Repeat with the remaining cookies.
Feel free to experiment with a variety of cookie cutter shapes, such as squares or stars.
Dip the cookie cutter lightly in flour before using it to prevent it from sticking too much to the dough.