Preheat the oven to 350 degrees.
Butter two 9" round cake pans, line with buttery parchment paper, sprinkle flour on them, and shake out the excess. If you have cake strips, you can use them to line pans.
Combine the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger in a mixing bowl.
Blend the vegetable oil, applesauce, eggs, granulated sugar, brown sugar, and vanilla in a large mixing bowl with an electric mixer.
Mix all dry ingredients together after adding them. Just enough carrots have been grated to distribute evenly. Pour mixture into 2 prepared cake pans in an even layer.
Bake for about 35 to 40 minutes in a preheated oven, or until a toothpick inserted in the center comes out clean.
After taking the cakes out of the oven, let them cool in the pan for ten minutes before inverting them onto a wire rack to complete cooling.
Cakes should be frosted and, if used, finished with chopped pecans. The cake should be refrigerated in an airtight container.