In a small bowl, mix together the dry cake mix, cream cheese, egg and butter until completely mixed. The dough will be very thick.
Press the dough into a greased 8x8 baking pan. Bake for 14-18 minutes. Remove from the oven and allow the bars to cool.
For the frosting: Using an electric mixer, mix the butter and cream cheese, scraping down the sides as needed, until the mixture is light and fluffy. This will take about 5 minutes. With the mixer on low speed, add the powdered sugar, 1/2 a cup at at time, until it is thoroughly mixed. Add the vanilla and beat the frosting on medium speed for about 3 minutes.
Frost the carrot cake bars with the frosting and top with the chopped walnuts.
We baked our bars for 14 minutes exactly and thought the texture was perfect (very soft). If you want them just a bit "cakier" or if your bars seem too "raw" for your liking, let them bake an additional 3-4 minutes.