Begin by browning the butter for the frosting. This will need to cool so we will start by browning the butter and setting it aside while we prepare the cake batter. Add 1 cup (2 sticks) of butter to a skillet over medium heat. Allow the butter to melt, then continue to cook until the butter becomes foamy and you begin to see browned bits on top of the foam. Remove from heat and add white chocolate. Gently whisk until the white chocolate is fully melted. (if needed, return the pan to the stove over low heat - be careful NOT to burn the chocolate)
Pour into a heat safe bowl and set aside. Let the mixture return to room temperature and solidify.
Preheat the oven to 350 degrees F. In a large bowl, combine cake flour, baking powder, baking soda, kosher salt, cinnamon, ground ginger, ground cloves, nutmeg, brown sugar, and sugar. Whisk together, then add the vegetable oil. Use an electric hand mixer to mix everything together until a thick paste forms, about 1-2 minutes.
In a separate bowl, combine eggs, egg yolk, maple syrup, vanilla extract, and sour cream. Whisk together until all ingredients are fully combined. Add the wet ingredients to the rest of the batter. Mix for 1-2 minutes, until a thick batter forms. Fold in grated carrots, canned pineapple (with the juice), and chopped pecans.
Spray 3 8-inch cake pans with nonstick baking spray. Divide the batter equally among the three pans and bake for 22-28 minutes, until a toothpick comes out of the center with just a few crumbs. Allow the cakes to cool in the pan for 10 minutes, then turn over onto a wire rack to cool completely.
While the cakes are cooling, continue to prepare the frosting. Add the cooled white chocolate/butter mixture to the bowl of a stand mixer fitted with the paddle attachment (it should be the texture of room temperature butter). Beat on medium speed for 2 minutes, then add powdered sugar, 1 cup at a time. After two cups have been added, beat on high speed for 20-30 seconds until the frosting smooths out (it will be very thick). Continue to add the powdered sugar until it's all added.
Once all of the powdered sugar is added, add vanilla extract, cinnamon, kosher salt, and cream cheese. Continue to mix until fluffy and smooth, about 1 minute. Scrape down the sides of the bowl and continue to mix for 30 seconds.
Once the cakes are cooled, place one of the cakes on a cake stand. Level the cake if needed. Spread an even layer of cream cheese frosting all around the cake then place the second cake on top. Add an even layer of frosting and repeat with the third layer. Add a thin layer of frosting around the cake and place into the refrigerator to set for 30 minutes (crumb coat).
Add the remaining frosting onto the cake and garnish with additional pecans or walnuts.
Notes
Usefreshly grated carrots instead of pre-shredded ones. Pre-shredded carrots are often too dry and lack flavor.
Mix the batter gently: Overmixing the batter can activate the gluten in the flour, resulting in a dense cake. Stir just until the ingredients are combined.
Let the cakes cool completely before frosting: Let the cake layers cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely. Frosting a warm cake is a recipe for disaster!
Store properly: Store the finished cake in an airtight container to retain its moisture. If making it ahead, wrap the unfrosted layers tightly in plastic wrap and refrigerate or freeze until ready to frost.