Add the carrots, the eggs and the oil in a blender and blend it for at least 5 minutes. In a bowl, mix flour, sugar and baking powder. Pour the carrot-egg-oil puree in to the dry ingredients mixture. Place in a 8-inch cake pan and bake for 45min at 350 F.
For the icing, just mix sugar, chocolate powder, milk and butter in a saucepan and mix it well. When it comes to a boil, wait 1 minute and turn off the heat.