Place the egg in a large mixing bowl and whisk with a fork.
Add the applesauce, vanilla, and raisins to the egg. Stir to combine.
Let raisins soak in applesauce & egg mixture for 20 minutes.
Preheat oven to 375 degrees F.
Add brown sugar and honey to the raisin mixture. Combine well.
In a separate bowl, whisk together flour, baking soda, baking powder, salt, and cinnamon.
Add flour mixture to raisin mixture in two increments, mixing well and scraping the bowl.
Fold in the Fiber One Bran Cereal.
Using a small scoop, drop dough onto a large cookie sheet. (Scoops should be heaping.)
Bake for 7 to 8 minutes.
Remove cookies from oven onto a cooling rack.
Mix powdered sugar with 1 tablespoon milk and stir well. Add more milk until sugar becomes a glaze. It should pour, but not be runny.
Drizzle glaze over cooled cookies. Let dry.
Store in an airtight container.