How to make it

1. Preheat your oven to 350°F (175°C). Grease a 9 x 5 in (23 x 13 cm) loaf pan and set aside.
2. In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
3. In a large bowl, beat together the granulated sugar, brown sugar, and eggs until light and fluffy.
4. Add the vegetable oil, applesauce, and vanilla extract to the sugar mixture and mix until combined.
5. Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
6. Fold in the grated carrots with a spatula until evenly distributed.
7. Pour the batter into the prepared loaf pan and smooth the top.
8. Bake for 50-55 minutes, or until a toothpick inserted into the center comes out clean.
9. While the bread cools, prepare the cream cheese frosting by beating the cream cheese and butter together until smooth.
10. Add the powdered sugar and vanilla extract, and beat until creamy and smooth.
11. Once the bread is completely cool, spread the cream cheese frosting over the top.