Preheat your oven to 375°F (190°C). Grease a muffin tin or line with paper liners.
In a large bowl, mix together the wheat bran and buttermilk. Let stand for 10 minutes.
In another bowl, whisk together the flour, baking powder, baking soda, and salt.
Stir the brown sugar, vegetable oil, egg, and vanilla extract into the bran mixture.
Add the dry ingredients to the wet ingredients and stir until just combined.
Spoon the batter into the prepared muffin tin, filling each cup about ⅔ full.
Bake in the preheated oven for 15-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for a few minutes, then transfer to a wire rack to cool completely.