In a mixer fitted with the paddle attachment, cream together butter, peanut butter, sugar and banana until smooth. Scrape down the bowl, and add the egg and vanilla. Mix just until combined.
Meanwhile, in a separate bowl, stir together cassava flour, gluten free AP flour, arrowroot, salt, and baking soda. Add this to the mixer, and mix, on low, until just combined. Add the chocolate chips, and mix just until combined. Scrape down the sides of the bowl, and mix on low speed until combined.
Using a ¼ cup scooper, scoop the cookie dough onto a parchment-lined baking sheet. Chill the dough for at least 30 minutes.
Before you are ready to bake, preheat the oven to 350°F. On a parchment lined baking sheet, place each cookie dough ball about 2-3 minutes apart. Gently press the dough down to flatten slightly. Bake for 10-12 minutes, turning the baking sheet halfway through baking. Remove from the oven, and let cool slightly before placing on a cooling rack to cool completely. ENJOY!