Preheat the oven to 350 degrees Fahrenheit. Spray a 9x13 glass baking dish with baking spray, or line it with parchment paper.
In a large bowl, whisk the dry ingredients together. (Flour, baking powder, baking soda, ground spices, and sea salt.)
In a separate large bowl, whisk the room temperature eggs until blended. Then whisk in the oil, then the sugars, applesauce, and vanilla.
After all of these ingredients are fully combined, slowly whisk the wet ingredients into the bowl of the dry ingredients. Finally, gently fold in the grated carrots. Be gentle, and don't overmix, to ensure fluffiness. :)
Pour the carrot cake mix into the prepared baking dish. Bake for 35-45 minutes, checking at about 35 minutes for doneness. (Using the toothpick method works ideally; insert into the middle of the cake, and if it comes out clean, the cake is done!)
Remove the cake from the oven, and allow it to cool in the baking dish for 20 minutes. Remove the cake from the dish, and transfer it to a wire rack for another 20 minutes to cool. You can make the frosting in the meantime. :)