Preheat your oven to 350°F and lightly spray a rimmed 18x13-inch baking sheet with non-stick cooking spray.
In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, and nutmeg for about 20 seconds to combine everything well. Set it aside.
In a large mixing bowl, whisk the granulated sugar and brown sugar together, breaking up any clumps of brown sugar with your fingertips if needed.
Add in the oil, applesauce, eggs, and vanilla. Use an electric hand mixer to blend until everything is fully combined and smooth.
Mix in the dry ingredients, then stir in the grated carrots until evenly distributed.
Pour the batter into your prepared baking sheet and spread it out into an even layer.
Bake for 25 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool completely before spreading on the cream cheese frosting. Just before serving, sprinkle with chopped pecans and add a carrot decoration if you like.
Store the cake in the refrigerator to keep it fresh.