How to Make It
Preheat oven to 400°.
Place 12 paper muffin cup liners in muffin cups; set aside. Combine brown sugar and butter in a medium bowl; beat with a mixer at medium-high speed until light and fluffy (about 5 minutes). Add egg; beat 1 minute or until well blended. Beat in egg white until well blended. Add milk, applesauce, molasses, and vanilla extract; beat on low speed until well blended.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, bran, baking powder, salt, and cinnamon in a large bowl; make a well in center of mixture. Add milk mixture to flour mixture, stirring just until moist. Gently stir in apples.
Spoon batter evenly into prepared muffin cups. Sprinkle evenly with turbinado sugar, if desired. Bake at 400° for 18 minutes or until muffins spring back when touched lightly in center.