Beat the cream cheese and butter together in a mixing bowl, for about 2 minutes. Add the powdered sugar and vanilla and beat until smooth. Spread on cooled cake.
This can also be baked in two 9-inch round or square cake pans if you'd like. I also like to place my 9x13 pan on a cookie sheet in the oven, this helps prevent the bottom from getting too brown before the center of the cake is done.
Also, for a variation, sometimes I had the zest of an orange to the cream cheese frosting, it's absolutely delicious!
I'm not a fan of nuts in baked goods, but I actually don't mind a few chopped pecans in carrot cake. Sometimes I add them, sometimes I don't. It's up to you if you want to add the nuts. You could also sprinkle the pecans on the frosting if you don't like them in the cake.