Heat the oven to 400 degrees Fahrenheit. Arrange paper liners in a standard muffin pan and apply a light coating of oil spray.
Crush the bananas in a large mixing bowl and verify that you have approximately 1 1/4 cups.
Combine the non-dairy milk, oil, sugar, vinegar, and vanilla in the bowl and whisk with the bananas until thoroughly incorporated.
Add the flour to the wet ingredients, then sprinkle the baking powder and salt over the top. Stir with a large spoon until just combined, taking care not to overmix. A few small lumps are acceptable.
Gently stir in the chopped walnuts or chocolate chips if preferred. Fill the muffin liners nearly to the top using a quarter-cup measure. Top with additional nuts or chocolate chips if desired.
Bake for 20 to 24 minutes until the top is golden and a toothpick inserted in the center comes out clean. Allow to cool in the pan for 5 minutes before transferring to a wire rack. Serve and enjoy.