1Preheat oven to 400 degrees F (200 degrees C). Line 12 muffin cups with paper liners.
2Mix bran cereal, flour, sugar, baking soda, cinnamon, and salt together in a bowl. Beat egg, buttermilk, and canola oil in a separate bowl. Pour liquid ingredients into bran mixture; gently stir in apple, carrot, and walnuts. Spoon batter into prepared muffin cups, filling them about 3/4 full.
3Bake in the preheated oven until a toothpick inserted into the center of a muffin comes out clean, 20 to 25 minutes. Cool in pans for 5 minutes before removing muffins to finish cooling on a wire rack.