Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

In a medium-sized bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.

In a large bowl, cream together brown sugar and eggs until light and fluffy. Gradually add applesauce, olive oil, and vanilla extract.

Carefully fold in dry ingredients into wet mixture, then add grated carrots, pecans, and raisins.

Divide batter into prepared pans and bake for 30-35 minutes until a toothpick comes out clean.

For frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar and vanilla until fluffy.

Once cakes are cooled, level the tops, frost between layers, and cover the entire cake with frosting.