1. In a small mixing bowl, pour the boiling water over the half cup of the All-Bran cereal. When cooled, mix in the applesauce and egg. If you add the egg too early, it will begin to cook over the hot cereal mixture. Shred 2 medium carrots using a box grater. Set aside.
2. While the water/bran mixture cools, mix together the flour, sugar, baking soda, baking powder and salt in a large mixing bowl. Stir in the raisins. Ensure that the raisins aren't clumped together; in fact the flour mixture should coat the raisins so that they are separate in the batter and don't sink to the bottom of the muffin when baking.
3. In a large measuring cup, combine the buttermilk and brown sugar, and stir into the dry ingredients.
4. Stir in remaining 1 1/2 cups cereal, the softened bran mixture and the shredded carrots. Cover the batter and refrigerate it overnight.
5. When you're ready to bake, preheat the oven to 375°F for 15 minutes. Grease the muffin cups with non-stick cooking spray.
6. Stir the batter once or twice, then scoop a heaping 1/4-cup of batter into each prepared muffin cup. If you prefer a less crispy exterior of the muffin, use muffin liners in your baking sheet.
7. Bake for 25 to 30 minutes, until a tester inserted in the center comes out clean.
8. Remove from the oven, cool in the pan on a rack for 10 minutes before removing the muffins from the pan.
9. These muffins last up to a week, refrigerated in a Ziplock bag; I usually pop them in the microwave before eating them.