Before making the make, dehydrate the carrots! If you have an air fryer with a dehydrate function, place the carrots on a piece of parchment paper in the air fryer, set to 190°F. Dehydrate for 2 hours, tossing occasionally. If you are using the oven, set the temperature to 175°F. Place the carrots on a parchment-lined baking sheet, and let dry for 2 hours, tossing every 15-20 minutes. Once the carrots are dried, remove from the air fryer or oven and set aside.
Preheat oven to 350°F. Lightly grease and flour (using the gluten free 1:1 flour!) 2 8-inch cake pans.
Place the sugar and butter, in a stand mixer fitted with the paddle attachment. Turn the mixer on high speed and cream until it is light and fluffy, scraping down the bowl as needed.
Add the eggs, one at a time, and mix until well combined. Meanwhile, in a small bowl, whisk together the gluten free all purpose flour, cassava flour, spices, baking powder, and salt. In a measuring cup, mix together the milk and vanilla extract.
Beginning and ending with the flour mixture, add ⅓ of the flour mixture. Mix until just combined, and add ½ of the milk mixture, mixing until just combined. Repeat with another ⅓ of the flour mixture and remaining milk mixture. Finally, add the remaining flour mixture, and mix until just combined, again scraping down the bowl as needed.
Divide the mixture evenly among the cake pans, and bake for 25-28 minutes, or until the cake springs back when gently pressed in the center (you can also insert a toothpick in the center, and pull the cakes from the oven when the toothpick comes out clean). Let the cakes cool in the pan for 10-15 minutes. Remove from the pan, and place on a cooling rack to cool completely. Once the cakes have cooled completely, use a serrated knife to cut them in half, crosswise. (NOTE: if you want to bake the cakes ahead of time, you can stop at this point, and wrap the cakes tightly in plastic wrap and place in the freezer. When you are ready to serve the cake, simply remove from the freezer about 2 hours before icing.)
While the cakes are cooling, prepare the frosting. Place the cream cheese in the bowl of a stand mixer fitted with the paddle attachment. Beat on high speed until it becomes smooth. Add the butter, and beat on high until well combined and smooth, scraping down the bowl as needed.
Add the powdered sugar, vanilla bean pod scrapings (or vanilla extract), and salt. Turn the mixer on low until all the sugar is incorporated. Scrape down the bowl, and then turn the mixer on medium for 2 minutes. Scrape down the bowl, and turn the mixer on high for 3-5 minutes, or until the frosting is light and fluffy. Add 1 cup dehydrated carrots to the frosting, and stir until just mixed
Before icing the cakes, make a quick simple syrup by bringin 1 cup of water and 1 cup of sugar to a simmer over medium high heat. Let simmer for about 10 minutes, and remove from the heat. Let cool slightly before using.
Once the cakes are cool, stack so all 4 layers on top of each other. Move the layers around to create as even a cake as possible. Remove the top 3 layers of cake and use a brush to brush the bottom layer of cake with a bit of simple syrup. Place about 1 cup of frosting on this layer of cake and spread evenly, to about ¼ inch from the edges. Repeat the process with the remaining layers of cake.
Once the cake is assembled with icing in the center of each layer, place in the refrigerator for about 10 minutes to allow the icing to set slightly. Remove from the refrigerator and place about 1 cup of icing on the top of the cake. Place a generous amount of icing on the sides of the cake, and then use an offset spatula to smooth the icing. Place about 2 cups of icing into a piping bag fitted with a piping tip of your choice. Pipe at the top edge of the cake and around the bottom, if desired. Sprinkle with dehydrated carrot shavings.