Step 1

Preheat oven to 350°. Spray 9x13 pan with cooking spray. I used a glass Pyrex pan.

Step 2

In a medium bowl, whisk together flour, xanthan gum, baking powder, baking soda, cinnamon, nutmeg, cloves, allspice, and salt. Set aside.

Step 3

In the bowl of your standing mixer, beat sugar, brown sugar and eggs on medium-high speed until thoroughly combined, about 45 seconds.

Step 4

Reduce speed to low, and slowly add the applesauce, oil, and melted butter. Mix on high for one minute, or until mixture is well mixed and light in color.

Step 5

Turn off mixer and stir in by hand the carrots and dry ingredients until no loose flour remains.

Step 6

Pour into greased 9x13 pan. Bake at 350° for 35-40 minutes or until a toothpick inserted into center of cake comes out clean. (Mine took 37 minutes.)

Step 7

Let cake cool, in pan, on a wire rack.

Step 8

In a mixing bowl, use a hand mixer to beat the softened cream cheese and butter for 3 minutes, or until soft, creamy and combined thoroughly.

Step 9

Add 2 cups of powdered sugar and beat until well mixed.

Step 10

Add the heavy cream or half and half, and pure vanilla extract. Beat on medium speed for 2 minutes.

Step 11

Add an additional 1/2 to 1 cup of powdered sugar until frosting reaches desired thickness and taste.

Step 12

Use a spatula or icing knife to spread frosting evenly over cooled cake. Slice into 15 large slices, or you can cut smaller slices if you prefer.