Use a 22 × 12 cm fluted or plain loaf tin. Coat tin with cooking spray. Preheat oven to 190°C.
Place the oats and walnuts on a baking tray; toast in the oven until the oats are golden brown and walnuts are crisp, about 7 minutes.
Combine flours, baking powder, bicarbonate of soda and salt in a bowl. Place the mashed banana, sugar, buttermilk, egg whites and oil in a separate large bowl. Stir to thoroughly combine. Fold in flour mixture and the oats and walnuts.
Spoon batter into the loaf pan. Bake 50–55 minutes or until a skewer inserted in the centre of the loaf comes out clean. Leave to cool in pan for 10 minutes; turn onto a wire rack to cool completely.
Store bananas in a paper bag at room temperature if they need ripening. Sliced bananas darken when exposed to air. To keep them from turning brown, toss the slices with a little citrus juice. To prevent bananas from overripening, store them in the refrigerator; the skin will turn black, but the bananas will be fine.