Preheat oven to 350°F. Lightly grease the bottom of a muffin pan or use muffin liners.
Add the mashed bananas, applesauce, oil, plant-based milk and vanilla to a large mixing bowl. Stir until well combined.
In a different medium-large mixing bowl, stir together the flour, bran, baking soda, baking powder, salt and cinnamon.
Add the dry mixture to the wet mixture and stir until just combined. Avoid overmixing.
Transfer the mixture to the prepared muffin pan, making 12 muffins. Top each muffins with the chopped walnuts. Bake for 20 minutes or until a toothpick inserted in the center comes out clean.
Let them cool a few minutes before removing from the pan.