Preheat your oven to 375°F (190°C). Grease a muffin tin or line with paper muffin liners.
In a large bowl, combine the bran cereal and milk. Let it sit for about 5 minutes until the cereal softens.
Add the mashed bananas, egg, vegetable oil, and brown sugar to the cereal mixture. Mix well.
In another bowl, whisk together the whole wheat flour, baking powder, baking soda, and salt.
Add the dry ingredients to the wet ingredients and stir until just combined. Do not overmix.
Divide the batter evenly among the muffin cups.
Bake for 18-20 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.