Preheat the oven to 350°F/180°C, grease 2 6-inch cake pans with non-stick baking spray, and line them with 6-inch parchment paper rounds. Grate the carrots using the small side of a box grater.
Add the all purpose flour, cake flour, sugar, brown sugar, baking soda, spices, and salt to the bowl of a stand mixer fitted with the paddle attachment. Mix on low, spinning about 5 times.
70 g all purpose flour, 60 g cake flour, 100 g granulated sugar, 50 g brown sugar, 1 teaspoon baking soda, 1 teaspoon ground cinnamon, ½ teaspoon ground ginger, ¼ teaspoon nutmeg, ⅛ teaspoon ground cloves, ⅛ teaspoon allspice, ¼ teaspoon sea salt
Add the butter to the bowl and beat on low for 5 minutes until the texture looks like wet sand.
85 g unsalted butter
Add the oil, eggs, and vanilla extract. Mix on low until a batter forms. Then add the applesauce and mix until well combined.
54 g vegetable oil, 2 large eggs, 1 teaspoon vanilla extract, 55 g applesauce
Mix in the carrots on low. Stop the mixer and gently fold in the walnuts with a rubber spatula.
150 g fresh grated carrots, 75 g chopped walnuts
Fill the prepared pans evenly and bake them for 20-25 minutes or until a toothpick comes out clean with a few moist crumbs.
Let the cakes cool in their pans for 10 minutes. Transfer to a wire rack and let cool completely.