Preheat oven to 350 degrees. Brush two 8-inch round cake pans with butter. Line with parchment; brush parchment with butter and dust with flour, tapping out excess.
Grate carrots using the coarse side of a box grater. Measure out 4 cups of carrots and transfer to a large bowl. Toss with candied ginger. In a separate bowl, stir together eggs, oil, and applesauce.
In a large bowl, whisk together dry ingredients. Using a rubber spatula, stir egg mixture into flour mixture until just incorporated. Gently stir in carrot mixture.
Transfer batter to prepared pans and bake until tester comes out clean, about 1 hour. Cool cakes in pans on a wire rack 20 minutes, then invert on to wire rack. Remove parchment, reinvert, and cool completely.