Preheat oven to 350 degrees F. Grease and flour a 9x5 inch loaf pan.
Whisk together mashed bananas, brown sugar, oil and almond or soy milk.
In a separate bowl, sift together the flour, baking powder, baking soda and salt.
Add the dry ingredients to the banana mixture and stir until evenly blended. Stir in the walnut pieces.
Pour batter into the prepared loaf tin, and spread to level.
Bake the banana bread for 45-50 minutes, until a tester inserted in the center of the loaf comes out clean. Cool the loaf for 20 minutes in the pan, then turn out to cool completely.
The banana bread will keep for up to 3 days at room temperature, or you can freeze it for up to 3 months. Do not refrigerate.