Preheat your oven to 350F and lightly oil a standard size loaf pan. Pour the almond or soy milk into a bowl and add the apple cider vinegar.
In a large bowl, mix together the flours, baking soda, baking powder, salt, and cinnamon.
Add the oil, sugar, mashed banana, and vanilla extract to the non-dairy milk and vinegar. Whisk to combine. Add these wet ingredients to the dry ingredients and mix till everything is evenly combined. Don't over-mix; some clumps are OK. Fold in the walnuts, if using.
Pour the batter into your prepared loaf pan. Sprinkle with extra walnuts, if you like. Bake the bread for 50-60 minutes, or until the entire loaf is a deep, golden brown color and a toothpick inserted into the bread comes out mostly clean. The top should be either flat or slightly domed; if it's not there yet, it's not quite ready. Check the bread at 45 minutes for doneness and continue checking until it's fully baked. If you feel that the bread is getting too dark as you bake, you can cover it with tented foil.
Transfer the loaf to a cooling rack and allow it to cool for 20-30 minutes. Gently remove the loaf from the pan and allow it to cool to room temperature before cutting into slices and enjoying.