Preheat your oven to 400°F (200°C).
Line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, and brown sugar.
In another bowl, mix the dairy-free yogurt, mashed bananas, oil, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients and mix until just combined. Do not overmix.
Divide the batter evenly among the muffin liners, filling them to the top for tall muffin tops.
Bake at 400°F (200°C) for 5 minutes, then reduce the temperature to 350°F (175°C) and bake for an additional 15-20 minutes, or until a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the tin for 10 minutes, then transfer to a wire rack to cool completely.