Preheat oven to 375°F (190°C). Grease a muffin tin or line with paper liners.
In a large bowl, combine bran cereal and buttermilk. Let sit for 10 minutes.
Add vegetable oil, egg, and brown sugar to the bran mixture. Mix well.
In another bowl, whisk together flour, baking powder, baking soda, and salt.
Add dry ingredients to wet ingredients and stir until just combined. Do not overmix.
Stir in vanilla extract.
Divide batter evenly among muffin cups.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Let muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.