Preheat oven to 400º. Line muffin tins with paper liners.
Combine 2 cups of All-Bran with 2 cups boiling water and set aside.
In a large mixing bowl, combine sugars, oil, and eggs. Add buttermilk and reserved softened All-Bran and mix well.
Add flour, baking soda, salt, and the remaining 4 cups of All-Bran. Mix until just combined. Mix in carrots or dried fruit if using.
Fill muffin cups about ⅔ full.
Bake for about 20 minutes or until a toothpick inserted into the muffin comes out clean.
Allow to cool slightly before removing to wire rack to finish cooling.
