Preheat oven to 350. Grease 2 9 - round cake plates with non-stick cooking spray and flour.
In a mixing bowl or stand mixer, beat together the eggs, oil, and sour cream until creamy. Beat in the sugar until smooth.
Add the cake flour, baking soda, baking powder, cinnamon, ginger and salt. Beat for 2 to 3 minutes, or until smooth batter forms. Fold in the shredded coconut and grated carrots. Pour the batter into the prepared baking dish.
Bake for 30 to 35 minutes, or until toothpick comes out clean. Let cool for 10 minutes on a cooling rack before removing the cake and placing on the serving platter.
To remove the cake, gently loosen the edges with a knife. Flip it onto a flat baking sheet, then flip it back right side up onto the serving platter. Let cool for at least an hour before frosting.