Cannery Carrot Cake

I made this for an Elder's Quorum activity. It was centered on being prepared. Roy was supposed to bring food and demonstrate an alternative cooking method. He made chicken in the dutch oven and I made this cake using dehydrated carrots from the cannery.
I adapted it from a recipe I found here as follows:
4 eggs
3/4 cups vegetable oil
1/2 cup applesauce
1 cup brown sugar
1 cup white sugar
2 cups flour
2 tsp. baking soda
2 tsp. baking powder
1/2 tsp. salt
2 1/2 - 3 tsp. cinnamon
1/4 tsp nutmeg
1 1/2 cups dehydrated carrots
1 1/2 cups cold water
1 cup chopped pecans (optional)

Frosting
1/2 cup butter, softened
8 oz cream cheese, softened
4 cups confectioners' sugar
1 tsp vanilla
1 cup chopped pecans (optional)

Prepare carrots by pulsing in food processor to grind into a course powder. Add 1 1/2 cups cold water. Set aside. (These need about 20 minutes to reconstitute. If needed add another 1/2 cup cold water.)
In large bowl, beat eggs, oil, applesauce, sugars and vanilla. In seperate bowl mix flour, baking soda, baking powder, salt, cinnamon, nutmeg. Mix two mixtures together. Fold in 3 cups of carrot mixture and pecans.
Pour into greased 9x13 pan. Bake in 350* oven for 40-50 minutes or until a toothpick inserted into the center of the cake comes out clean. Let cool. If desired, turn out onto cooling rack after 10 minutes and cool completely.
To make frosting: Whip butter, cream cheese, sugar and vanilla until smooth and creamy. Stir in pecans and frost the cooled cake.