Preheat the oven to 350 degrees. Line two baking sheets with parchment paper.
In a stand mixer cream together the butter, peanut butter, sugar, and brown sugar on medium speed until light and fluffy, about 3 minutes. Add the egg and vanilla, mix to combine.
In a small bowl whisk together the peanut flour, salt, and baking soda. Add the mixture to the creamed butter mixture and mix on low speed until just smooth. Add the chocolate pieces and mix on low until just combined.
Use a 2-ounce scoop to portion out the cookies or use a spoon and then roll the dough in your hands to make it round. Sprinkle the cookies with sugar and flatten with the tines of a fork to create the classic cross hatch pattern.
Bake for about 8 to 10 minutes, making sure they are set, but not quite dry in the center. Cool on a rack.