Preheat oven to 325^F. Prepare three 9 inch round cake pans- grease and flour or line with parchment.
Stir together flour, baking powder, baking soda, cinnamon, nutmeg, salt. Set aside.
In large mixing bowl, whisk together eggs and sugar until light and airy. Whisk in oil and applesauce.
Stir in carrots, pineapple (with juice), and pecans (optional). Then fold in the dry ingredients. Evenly divide batter into prepared pans and smooth tops.
Bake for 45 minutes, until layers are golden and a toothpick inserted in center comes out clean.
Cool cake in pans for 10 minutes, then invert onto cooling racks until completely cooled. Remove parchment paper before icing.
To make icing: In a stand mixer or use a hand mixer (or your muscles if you are brave!) use the paddle attachment and beat the cream cheese, butter, and vanilla on medium speed until very soft and light- about 5 minutes. Decrease the mixer speed to low and gradually beat in the powdered sugar. Once all sugar is incorporated, increase speed to medium and beat 5 minutes longer.
To assemble cake, place on layer on platter or cardboard round and spread with 1/3 of the icing. Top with another layer and spread another 1/3 icing on. Place last layer on top, bottom side up, and use an offset spatula to frost the tops and sides of the cake with remaining icing. Sprinkle toasted pecans on top and press into sides of cake if desired.