Preheat your oven to 375°F (190°C). Grease a muffin tin or line with paper liners.
In a large bowl, combine the bran cereal and buttermilk. Let it sit for about 10 minutes to soften.
In another bowl, whisk together the oil, egg, and brown sugar until well combined.
Add the wet ingredients to the bran mixture and stir to combine.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Do not overmix.
Stir in the vanilla extract.
Divide the batter evenly among the prepared muffin cups.
Bake for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the tin for a few minutes before transferring to a wire rack to cool completely.