Warm the Oven: Set the oven to 375 degrees Fahrenheit. Line a muffin pan with paper liners or grease each cup lightly. This keeps the muffins from sticking and helps them bake evenly.
Soften the Bran: Pour the milk over the bran in a large bowl. Stir gently and let it sit for five minutes. This step softens the bran and keeps the muffins moist.
Add the Wet Ingredients: Stir melted butter, honey, egg, and vanilla into the bran mixture. Mix until everything blends smoothly and looks creamy.
Mix the Dry Ingredients: In another bowl, combine flour, brown sugar, baking soda, and salt. Stir well so the leavening spreads evenly.
Combine the Batter: Add the dry mixture into the wet ingredients. Stir just until combined. The batter should look thick but scoopable.
Fill the Muffin Pan: Spoon the batter into each muffin cup, filling about three quarters full. This gives space for the muffins to rise nicely.
Bake Until Ready: Place the pan in the oven and bake for eighteen to twenty minutes. The tops should feel firm and spring back when touched lightly.
Cool Briefly: Let the muffins rest in the pan for five minutes. Transfer to a rack so they cool evenly and keep their shape.