Prep Your Pan: Preheat your oven to 400°F (200°C). Line a 12-cup muffin tin with paper liners and lightly spray the insides with nonstick cooking spray.
Combine the Dry Ingredients: In a large bowl, whisk together the wheat bran, whole wheat flour, baking powder, baking soda, salt, and cinnamon. Set aside.
Mix the Wet Ingredients: Stir vinegar into milk and set aside to curdle. In a large bowl, whisk brown sugar, molasses, applesauce, and eggs until smooth. Pour in the curdled milk and whisk again until blended.
Bring the Batter Together: Add the dry ingredients to the wet mixture. Gently fold with a spatula until just combined (a few streaks of flour are okay). Stir in the neutral olive oil or softened butter until the batter is evenly blended. If using raisins, blueberries, or pecans, fold them in now.
Fill and Bake: Divide the batter evenly among the 12 prepared muffin cups. Each should be about ¾ full. Bake for 16-18 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs. (I like to use Tulip Cupcake Liners )
Cool and Serve: Let the muffins cool in the pan for 5 minutes. Transfer to a wire rack to finish cooling. Enjoy warm, plain, or with a little butter spread on top.