For a 6 inch cake, grease three 6-inch cake pans and line the bottoms with a circle of parchment paper.For an 8 inch cake, grease two-three 8-inch cake pans (depending on how thick you want each layer) and line the bottoms with a circle of parchment paper. Grate peeled carrots until you reach 2 ¼ packed cups or use a food processor (hand-grating the carrots will give you finer shreds while blending them will be a little chunkier).
Using a stand mixer, beat the oil, brown sugar, and eggs together on high speed using the whisk attachment. Let it mix while you measure out the dry ingredients. In a medium-large bowl, whisk the GF flour, cinnamon, nutmeg, cloves, salt, and baking powder together. Add half of the dry mixture to the well beaten oil-sugar-egg mixture and whisk on low speed. Slowly turn the speed up to high. Lower the speed again, add the vanilla and the milk and beat on high until incorporated. Add the rest of the dry ingredients and mix well. Scrape the sides and bottom of the mixing bowl with a spatula. Add all the shredded carrots and mix on high for a minute.
Evenly distribute the batter between the 2-3 prepared cake pans. Bake for 20-35 minutes or until a toothpick comes out clean after being inserted into the center each cake layer. Remove from the oven and let the cake layers cool completely.
While the cake layers are baking... in a small saucepan, bring the butter and brown sugar to a boil over medium heat, stirring frequently to prevent burning. Let it boil for 1 minute or until thickened and the mixture starts to bubble upwards in the pot. Quickly, pour the hot mixture into the bowl of a stand mixer. Add the salt, vanilla, and cream cheese then and whip on medium-speed (using the whisk attachment) until everything is fully combined. Add the powdered sugar and mix well. Scrape the sides and bottom of the bowl with a spatula, then give it another good mix. Set the bowl of runny frosting in the fridge to chill while the cake layers are baking and cooling.
When the cake layers are completely cool, remove the frosting from the fridge. If it is still runny, chill in the freezer for 15-30 minutes. Once chilled (and no longer runny), mix very well on high speed (about 2 minutes or longer) until fluffy and lightened in color. If necessary, trim off the domed tops of the cake layers using a bread knife, to create flat layers.
Add a small dollop of frosting onto a plate. Place one of the cake layers on the dollop.
Spread some frosting (not too much) onto the layer. Stack another cake layer on top.
Repeat step 8 if you are making a triple layer cake. Spread as much of the remaining frosting as you wish on the top and sides of the cake. I went for a thin layer of frosting on the edges for a semi-naked look. You probably won't have leftover frosting for piping decorations, especially if you are making an 8 inch cake. At this point you can decorate the cake however you wish. I decorated mine with whole cloves, ground cinnamon, and turbinado cane sugar. If you decorate with cloves, they are just for looks and don't taste good whole, so I recommend taking them off or warning people to do it themselves!
Slice, serve, and savor every bite!
