Preheat the oven to 175°C (350°F) and grease two 23cm (9-inch) round cake tins, lining the bases with parchment paper.

Spread the pecans on a baking sheet and toast for 7–8 minutes until fragrant, then chop once cooled.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves.

In a large mixing bowl, whisk the light brown sugar, granulated sugar, vegetable oil, eggs, applesauce, and vanilla extract until the mixture is completely smooth and emulsified.

Gradually fold the dry ingredient mixture into the wet ingredients using a spatula until no dry flour pockets remain.

Incorporate the grated carrots and the 130g of chopped pecans into the batter using a gentle folding motion.

Distribute the batter evenly between the prepared cake tins and smooth the surfaces with a spatula.

Bake for 30–35 minutes, or until a skewer inserted into the center of the cakes comes out clean.

Allow the cakes to cool in the tins for 10 minutes before transferring to a wire rack to cool completely to room temperature.

Prepare the frosting by beating the softened cream cheese and butter together until aerated and smooth.

Add the icing sugar, vanilla extract, and lime zest, beating on low speed until incorporated and then on high until light and fluffy.

Place one cake layer on a stand, apply a layer of frosting, top with the second cake, and cover the exterior and top with the remaining frosting.