Using a food processor, blender or hand grater, shred the carrots. Set them aside while you prepare the batter.
Into a small bowl sift together flour, granulated sugar, cocoa powder, salt, baking powder, and baking soda. Although you might be tempted to skip the sifting step, I recommend that you do sift the ingredients together - the texture of the cake will be much smoother.
In the large bowl of an electric mixer, beat together the eggs and oil on low speed until just combined. Add the flour mixture and beat until just combined. Stir in carrots and put the batter in the prepared pan. Bake cake in the middle third of the oven for 50 minutes, or until a tester comes out clean. Cool cake in pan on a rack 10 minutes and invert onto rack to cool completely.
Sprinkle with confectioner's sugar, if desired.