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 sit for 10 minutes.
Stir in the vegetable oil, beaten egg, brown sugar, and vanilla extract.
In another bowl, whisk together the flour, baking powder, baking soda, and salt.
Add the dry ingredients to the wet ingredients and stir until just combined.
Divide the batter evenly among the muffin cups.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.