Preheat the oven to 350 F, grease a 9x13 inch pan with butter and dust with flour. Do not skip this step! You can alternatively use three 9 inch pans.
In a small bowl, stir together the dry ingredients (flour, baking powder, baking soda, salt, cinnamon, nutmeg and allspice) and set aside.
In another bowl, toss the carrots with the lemon juice and set aside.
In a large bowl, blend the sugar, oil, vanilla and eggs until smooth.
Add the flour mixture, stirring just to combine.
Fold in the carrot mixture and nuts. The nuts are optional, but I highly recommend adding them!
Pour the mixture into the prepared pan and bake for 45-60 minutes (if baking multiple layers, the baking time will need to be adjusted accordingly), or until a toothpick inserted comes out clean. Cool completely before frosting.
TO MAKE THE FROSTING:
To make the frosting, blend together the butter, cream cheese, vanilla and lemon juice.
Gradually add in the powdered sugar and beat until smooth and fluffy. The frosting should hold a soft peak when you lift up the whisk/beater.
I like to garnish the cake with some cinnamon and chopped nuts, but this is totally optional.
Notes
Source: Hot Chocolate Hits with permission to share her new cookbook. I did double the frosting.