Royal icing dripping over the sides makes for a dramatic presentation and makes this carrot cake ideal for a wedding shower or other special occasion. The cake is moist and delicious, with the carrots pureed rather than simply grated, and with orange zest and juice lending bright flavor. Royal icing is made by whisking an egg white until foamy and then whisking in the powdered sugar; here it's flavored with a bit of lemon juice. Use it immediately, before it has a chance to harden.