*If you want to top with the candied carrots, I’d recommend making them the day before so they have lots of time to dry before assembly
Make your carrot topping: Lay 2 of your carrots flat and peel them into strips. Grate the remaining carrot. Place sugar and water in a pot and bring to a simmer. Once simmering, add your peeled carrots first and simmer for 8 minutes until soft and slightly translucent. Remove with a slotted spoon and lay on a paper towel to dry and cool slightly. Bring the liquid back to a simmer and add your shredded carrots, and simmer for 3 minutes. Transferring to a paper towel to dry. Once your carrot strips are cool, roll up starting at the skinniest end, to form rosettes. For larger roses, line a few strips vertically, slightly overlapping one to the next, before rolling. Place rosettes on a parchment-lined baking sheet and bake for 20 minutes at 200°F to lightly dry out. Repeat with grated carrots, then leave them uncovered overnight.
Brown the butter for your frosting by placing your butter into a small pot over medium heat. Swirl the pan every minute or so. As the mixture begins to separate, the milk solids will rise and then slowly drop to the bottom of the pot and begin to brown. Once browned, remove from the heat and pour immediately into a bowl. Leave to sit at room temperature for 10 minutes before moving to the fridge to set while you bake your cakes
Preheat oven to 350°F. Grease two 9-inch round cake pans and line the bottoms with parchment paper
In a bowl, sift together your flour, cinnamon, nutmeg, salt, baking soda, and baking powder. Stir and set aside
In another bowl, beat together your sugars, coconut oil, and applesauce for a minute until combined
Add in two of your eggs, mix them in completely, then add the remaining two eggs. Mix in your grated carrots and orange zest
Mix in your dry ingredients until just combined. Do not overmix.
Split your batter between your lined cake pans and bake for 25-30 minutes until a toothpick inserted into the center comes out clean
Remove from the oven and allow to cool in the pans for 10 minutes before inverting onto a wire rack to cool completely (remove parchment paper from the bottom of the cake)
While your cake cools, finish making your cream cheese frosting. Once your butter has softened to room temperature and is no longer melted or liquid, add it to a mixing bowl. Add your room-temperature cream cheese and beat for a minute until smooth. Sift your powdered sugar into the bowl and carefully beat until all is incorporated. Add the milk and give one final beat. Keep at room temperature while you prepare the cake (this will make it easier to spread)
To form your bunny, place one of your cake rounds on a cutting board and cut out your ears and bowtie. It will look kind of like a tennis ball when you cut it. To do this, at the bottom of your round, about a third of the way up, cut a line curving downward from one side to the other. Now you have one ear and the bottom of your bow tie! From the top of your round, about a third of the way down a line curving upward, from one side to the next. You should see two bunny ears (top and bottom of your round) and a bowtie in the middle. On a large cookie sheet or tray, place your bowtie at the bottom. Then, above the bow tie, fit your remaining 9-inch round that hasn’t been cut – this is your face! Lastly, place one of your bunny ears on either side of the face. Now you have your bunny!
Frost all over with the cream cheese frosting and top with the shredded and rosetted carrots. Enjoy!