Preheat oven to 200 C (390 F) and line a baking tray with baking paper.
Puree the banana. I used two small bananas and got 1/2 cup of puree.
Whisk banana and egg together in a mixing bowl.
Add flour and mix until a smooth dough forms.
Lightly flour a clean surface and a rolling pin, and roll the dough out to about 1/2 cm thick.
Use cookie cutters to cut out round cookies. My cookie cutter was about 6cm across.
Re-roll the extra dough out again and continue cutting out cookies until you have used up all the dough.
Place cookies on prepared baking tray, evenly spaced.
Bake for approximately 10 mins, or until they are just starting to turn golden brown.
Makes about 12.