Preheat the oven to 350 degrees Fahrenheit (180 degrees Celsius). Line a 9-inch springform pan with parchment paper and set aside.
Grate your carrots and apples using a box grater or a coarse grater and set aside.
Add all purpose flour, sugar, brown sugar, baking soda, spices, and salt to the bowl of a stand mixer fitted with the paddle attachment (or a large bowl with a handheld electric mixer). Mix on low speed until combined.
130 grams all purpose flour, 100 grams granulated sugar, 50 grams light brown sugar, 1 teaspoon baking soda, 2 teaspoons ground cinnamon, ½ teaspoon ground cardamom, ½ teaspoon ground ginger, ¼ teaspoon ground nutmeg, ¼ teaspoon ground cloves, ¼ teaspoon allspice, ½ teaspoon salt
Add the butter to the flour mixture and beat it in on low for 5 minutes until the mixture looks like wet sand. The butter should be no larger than pea-sized pieces.
5 tablespoons unsalted butter
Mix in the oil, eggs, and vanilla extract on low speed until a thick batter forms. Scrape down the sides of the bowl with a if needed and beat in the applesauce.
54 grams vegetable oil, 2 large eggs, 1 teaspoon vanilla extract, 50 grams unsweetened apple sauce
Add the carrots and apples to the batter, gently folding them in with a rubber spatula until evenly distributed throughout the batter.
100 grams fresh grated carrots, 100 grams shredded apples
Pour the batter into the prepared pan. Bake for 28-32 minutes until a toothpick or cake tester inserted in the center comes out clean with just a few moist crumbs attached. Crumbs mean it's still moist!
Carefully remove the cake from the oven and let it cool for 5-10. Release the sides and transfer the cake to a wire rack and cool completely for about 30 minutes.
Burnt Honey Cream Cheese Frosting
Add honey to a small saucepan on medium heat. Cook for about 10 minutes until it turns a dark amber color and smells burnt. It will bubble viciously, so occasionally mix to keep it from overflowing. Take off the heat to cool slightly (but not too long because it will solidify).
43 grams honey
While the honey cools, beat the room temperature butter and cream cheese together in a large bowl on medium-high speed until creamy.
Scrape down the sides of the bowl and beat in the vanilla, salt, and honey on medium speed until evenly combined.
½ teaspoon vanilla extract, ¼ teaspoon salt
Mix in the powdered sugar on low speed 1 cup at a time until combined. Then increase to medium and beat until light and fluffy.
180 grams powdered sugar
Spread or pipe frosting on top of the cooled cake and garnish with toasted nuts or coconut. Slice and enjoy!
Notes
Freshly shred your carrots. Pre-packaged shredded carrots are too thick and dry and won't give the cake moisture.It is ok if the grated apples turn into something that looks like applesauce! Use firm apples for the best results (like Granny Smith).Use room temperature dairy ingredients for a smooth frosting and cake batter that bakes up evenly. Set the dairy ingredients and eggs on the counter 1-2 hours before baking to warm up.Let the cake cool completely. If you frost the cake while it's still warm, the frosting will melt off.