Preheat oven to 350 degrees. Butter a nine-inch-square baking pan.
Cream butter, add sugar and beat in egg. Stir in banana puree & vanilla. In a seperate bowl, combine flour, baking soda, and cinnamon. Add dry ingredients to wet until just combined.
Add cinnamon chips and walnuts and bake for 25 minutes. Remove from oven and allow to cool before cutting into squares.