Preheat the oven to 350ºF (177ºF) and prepare three 6-inch or two 8-inch cake pans by spraying the sides with baking spray and fitting a parchment paper circle to the bottoms.

Grate the carrots by hand and measure them out into a medium bowl. Set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves. In another medium bowl, whisk together the white and brown sugars, vegetable oil, eggs, applesauce, and vanilla.

Add the wet ingredients to the dry ingredients and fold together using a rubber spatula until just combined, then fold in the grated carrots.

Pour the batter evenly between the prepared cake pans and bake for 35-40 minutes, or until a toothpick inserted comes out clean. Allow the cakes to cool in the pan for 10 minutes before turning them out to cool fully on a wire rack or baking sheet.

Brown the Butter: Add the butter into a large frying pan and cook over medium heat until the butter melts, stirring occasionally. Continue cooking for another 5-7 minutes while stirring constantly. The melted butter will start to foam on top, then will turn light brown in color and smell deliciously nutty. Remove from heat and transfer to a glass container. Allow it to re-solidify for about 2-3 hours at room temperature or place it into the refrigerator for about 1-1.5 hours.

When the brown butter has cooled to the ideal consistency, place it into the bowl of your stand mixer fitted with a paddle attachment and add the cream cheese. Mix on medium-high until fluffy and light in color, about 5 minutes.

Turn the mixer to low speed and add the powdered sugar a few cups at a time, scraping down the bowl and paddle after mixing in each addition. Add the vanilla and salt and continue mixing on low speed until smooth and uniform.

In a small saucepan, add the brown sugar, cinnamon, salt, vanilla, and water. Mix together while you cook over medium heat until the mixture starts to bubble slightly. Reduce the heat slightly and add the pecans. Stir to coat them while you continue cooking for another 2-3 minutes, until the pecans are nicely coated and smell fragrant.

Place the candied pecans onto a parchment lined baking sheet in a single layer to cool until room temperature, about 10 minutes.

Once the cake layers have cooled completely, level them to your desired height. Fill and stack the cake layers with brown butter cream cheese frosting, then crumb coat the cake with more brown butter cream cheese frosting. Refrigerate the crumb coated cake for at least 30 minutes to let the frosting firm up.

To create the design pictured, use the cream cheese frosting to frost a rustic finish on the cake. If using, press some of the candied pecans around the bottom third of the cake. Add the rest of the buttercream into a piping bag fitted with Wilton Tip 1M and pipe a swirl border on top of the cake. Garnish with more candied pecans.