Wash hands with soap and water for 20 seconds.
Do not taste or eat any raw dough or batter made with uncooked flour and/or raw eggs.
Preheat the oven to 350°F with a rack in the center position. Lightly grease a 9" x 5" loaf pan; if your pan is glass or stoneware, reduce the oven temperature to 325°F.
In a large bowl, mash the bananas. Measure 2 cups.
In a large bowl, stir together the mashed banana, oil, sugar, eggs, and vanilla.
Measure the flours by gently spooning them into a cup, then sweeping off any excess. Mix the flours, baking soda, baking powder, salt, cinnamon, and chopped walnuts into the banana mixture. Scrape the bottom and sides of the bowl and mix again to thoroughly combine the ingredients.
Spread the batter into the prepared pan.
Mix together the sugar and cinnamon, and sprinkle over the batter.
Bake the bread for about 60 to 75 minutes, until the bread feels set on the top, and a paring knife (or other thin knife) inserted into the center comes out clean, or with just a few moist crumbs (but no wet batter). If you have a digital thermometer, the bread's temperature at the center should register about 205°F. If the bread appears to be browning too quickly, tent it with aluminum foil for the final 15 to 20 minutes of baking. Note: If baking in a glass or stoneware pan, increase the baking time by 10 to 15 minutes.
Remove the bread from the oven. Cool it in the pan for 15 minutes, then loosen the edges, and turn it out of the pan onto a rack to cool completely.