Preheat your oven to 350 degrees Fahrenheit and grease two standard (9-inch by 5-inch) loaf pans with vegan butter, lining them with parchment paper if desired.
In a large mixing bowl, mash the bananas with a fork until no large pieces remain.
Add the sugar, applesauce, oil, dairy-free milk, and vanilla and mix until everything is incorporated.
Measure the flour, baking soda and salt into a separate mixing bowl and stir them together. Once they’re mixed together, dump the dry ingredients into the wet ingredients.
Carefully mix the wet and the dry ingredients together. The danger here is over-mixing which will result in a dense, flat and dry loaf. The best technique for mixing is to scoop underneath the mixture and pull up gently instead of stirring around in a circle (like you’d stir your coffee, for example). Continue mixing this way just until the dry ingredients have been incorporated. It’s fine if there are a few small streaks of flour in the batter; it’s the large pockets of flour you want to make sure are incorporated.
Pour the batter into the prepared loaf tins, smoothing out on tops.
Bake the loaves in the oven at 350 degrees for about 45-55 minutes (depending on your oven), or until they're golden brown on top and a toothpick inserted into the centre of the loaf comes out clean.
Let the loaves cool in the pan for about 10 minutes and then lift them out of the pan using the parchment paper (or turn them out gently if you didn't use the parchment paper) to cool completely on a wire rack.
Slice and enjoy!