Preheat oven to 350°F and grease a 13×18 inch jelly roll or sheet pan. Line with parchment paper.
In a large mixing bowl, mix the sugar and oil together. Beat in the eggs.
In a separate bowl, whisk the flour, cinnamon, baking soda, allspice, salt and baking powder.
Add the dry ingredients and mix until combined. Fold in the carrots and then spread into the greased pan. Bake for 15 to 20 minutes or until toothpick comes out clean.
For the frosting:
Beat the cream cheese and butter together. Mix in the powdered sugar and cream until smooth. Add a tablespoon or two of cold water. Mix in the vanilla and then spread over cooled cake.