In a large bowl, mash the banana as smooth as possible. Beat in eggs until fully incorporated, then beat in peanut butter. Once smooth, add the chickpea flour, coconut flour and baking soda, and start to fold together with a spatula.
It will likely be tough to get everything incorporated with just a spatula, so switch to using your hands to finish kneading the dough. Once all the flour has been folded into the dough, transfer it to a flat, parchment lined surface and roll it out to 1/4" thick. You might have to sprinkle with a little flour if the rolling pin starts to stick.
Cut the dough into whatever shapes you want (I used this dog bone cookie cutter) and place on a baking sheet. Bake for 14 minutes until the treats are golden brown. Remove from oven and let cool completely before serving to your doggie (or packing up as a gift).