Preheat oven to 350 degrees F. Spray a 9x5 loaf pan with nonstick spray.
In a large mixing bowl, combine grated carrots, oil, applesauce, pureed carrots, egg, and vanilla. Mix thoroughly.
Beat sugars into the mix until creamed.
Add flours, baking soda, baking powder, salt, and pumpkin pie spice. Mix until blended. Stir in nuts and raisins.
Pour batter into prepared pan.
Bake for about 45 minutes, or until bread is brown and springs back when gently pressed in the middle.
Remove bread from pan and cool on a wire rack.
Just before serving, make the glaze by whisking together cream cheese, milk, and powdered sugar in a small bowl.
Drizzle the glaze over top.