In a food processor, process sugar for 30-45 seconds to make superfine sugar (not powdered!)
Add in cold butter pieces and process for another 30-45 seconds. Until the butter and sugar are just combined.
Add in egg and vanilla extract. Process until just combined. You may need to scrape down the sides at least once.
Divide batter in half. Place half of the batter back into the food processor.
Add in peanut butter, 1 ½ cups flour, ⅛ teaspoon baking soda and an ⅛ teaspoon baking powder. Process until combined.
Remove dough from mixture, place on a piece of parchment paper and then place another piece of parchment paper over it. Roll out the peanut butter dough until you have the size of large rectangle. I like to roll it out in between the two pieces of parchment paper so the dough doesn’t stick to the rolling pin. Set aside.
Place other half of dough into the food processor and add in the cocoa powder, espresso powder, if using, remaining 1 ½ cups flour, ⅛ teaspoon baking soda and ⅛ teaspoon baking powder.
Process until well combined then remove from the processor and roll out the same as you did with the peanut butter dough.
Refrigerate the flattened doughs for at least 1.5 hrs.
Then remove dough from the refrigerator and preheat your oven to 300°F and line a baking sheet with parchment paper.
Using a sharp knife, trim the dough to have straight edges and are roughly the same size. Mine were about 9 inches long by 7 inch high.
You want the chocolate rectangle slightly smaller in height than the peanut butter so trim accordingly.
Place the chocolate rectangle on top of the peanut butter rectangle making sure the bottoms match up. Since the chocolate dough is slightly shorter than the peanut butter dough, they won’t match up exactly (see picture in post above).
Starting from the bottom roll the dough up to the unevenly matched top. Using the parchment paper to roll the dough will help. If the dough cracks as you roll it don’t worry. Just smooth and pinch it back together as you roll.
Once it is rolled up completely cut the log in half and place each half side by side, slightly pinching them together (see picture in post above). Gently slice the rolled cookie dough halves and then gently press the dough together and pinch the middle to form more developed wings.
Place cookies on parchment lined baking sheet. Refrigerate the rest of the dough while you aren't using it.
Bake for 18-20 minutes, or until edges just start to turn golden. I recommend baking on the second to lowest rack in your oven. Depending on how thick you cut your cookies will alter how long you need to cook them (thicker cookies need more baking time, thinner need less).
Use the cookie dough scraps to make marbled sugar cookies. Just mix the leftover dough together by hand and then form into balls. Smash flat and bake on a cookie sheet same as you did with the butterfly cookies.
If you are wanting to frost the cookies you can find the icing recipe here!