Preheat oven to 350 degrees and line a square (9x9 or 8x8) baking dish with parchment by paper.
In a large mixing bowl combine the flour, sugar, baking powder, baking soda and salt.
Add the softened butter one tablespoon at a time mixing on low speed until no large chunks of butter remain
Add the egg and mashed banana, mix to combine
Slowly add the buttermilk, mixing on low speed. Add the vanilla and oil and mix until smooth. Fold in the walnuts
Spread the batter into the prepared pan and bake 30-40 minutes.
To make the frosting beat the butter, powdered sugar and walnut butter together until light and fluffy. If the frosting is too thick add milk one tablespoon at a time.
Spread the frosting over the cooled cake and decorate with more chopped walnuts