Follow the steps in order for the best result.
Begin by preheating your oven to 375 degrees Fahrenheit (190 degrees Celsius).
In a large mixing bowl, thoroughly combine the all-bran cereal, mashed bananas, and milk. Allow this mixture to stand for 5 minutes to soften the bran.
Introduce the brown sugar, vegetable oil, beaten egg, and vanilla extract to the bran mixture. Ensure all ingredients are well incorporated.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt to evenly distribute the leavening agent and seasoning.
Gently fold the dry ingredients into the wet bran mixture, stirring only until just combined. Be careful not to overmix, as this can result in tough muffins.
Line a muffin pan with paper liners, or grease the pan well to prevent sticking. Spoon the batter evenly into the prepared muffin cups, filling each about two-thirds full.
Bake in the preheated oven for 20 to 25 minutes, or until a wooden skewer inserted into the center of a muffin comes out clean. Let the muffins cool in the pan for a few minutes before transferring them to a wire rack to cool completely.