The ingredients should be at room temperature.
Prepare your 8-inch / 20-cm cake pan / springform pan. You can bake the cake in 1, 2 or 3 pans (read more in notes!). If you want to bake the cake in one pan, it must be an extra deep/high rim pan (3-inch / 7.5 cm, measured in the inside). Line the bottom of the pan with baking paper and butter its sides. Set aside.
Prepare all the ingredients, then set the oven to 320°F / 160°C / Gas Mark 3, no fan (if you have a convection oven, reduce the temperature by 20°).
Mix all the dry ingredients together: flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger and cloves (you can grind them in a coffee grinder or using a pestle and mortar).
Mix all wet ingredients together: grated carrots, oil, applesauce, eggs, white and brown sugar, vanilla extract, chopped nuts.
Add the dry ingredients to the wet ingredients and whisk until combined, but be careful not to overmix the batter.
Pour the batter into the prepared cake pan. If using more than 1 cake pan, divide the batter evenly into the pans. If you‘re baking the cake in three pans bake the cakes for 45 minutes, if baking in one pan - bake for 1h 30 min - 1h 45min. At the end of the baking time, if the cake starts to brown too much, you can cover it loosely with a piece of aluminum foil. The cake is ready when a wooden stick inserted into the center of the cake comes out clean.
After putting the cake in the oven, start making the frosting.