Preheat Oven and Prep Pan:
Heat oven to 375°F (190°C). Insert paper liners into a 12-cup muffin pan or coat with nonstick spray.Hydrate Wheat Bran:
Combine wheat bran and buttermilk in a bowl; let rest to hydrate the bran.Mix Wet Ingredients:
Mix applesauce, brown sugar, egg, cinnamon, and vanilla until uniform.Fold in Dry Ingredients:
Gently incorporate flour, baking powder, baking soda, and salt until barely combined; batter should remain lumpy.Fill Muffin Cups:
Portion batter equally into muffin cups (the batter is stiff).Bake Muffins:
Bake 18 minutes, checking at 16 minutes; a toothpick inserted into the center should emerge clean or with a few crumbs.Cool Muffins:
Let cool in the pan briefly, then move to a wire rack for complete cooling.