Preheat the oven to 350 degrees F. Line 2 sheet pans with a silicone baking mat or parchment paper and set aside. Alternatively, you can do this in 2 batches.
Sift flour, baking soda, and baking powder together and set aside. In the bowl of an electric mixer, blend butter, banana, and peanut butter together. Add egg substitute, brown sugar, and sugar substitute and beat until incorporated. Gradually add the sifted flour mixture to the mixer and continue to mix on low speed until incorporated.
Drop batter, in 1 tablespoon-size balls, onto the prepared sheet pan, about 2 inches apart. Flatten cookies a little with the back of a fork. Bake for 10 minutes or until golden brown and crispy. Let cool on a metal rack.