• Preheat the oven to 350°F / 177°C. Butter a 13"x9" cake pan, and line the bottom with parchment paper. Butter the parchment paper and flour the pan inside, being sure to bang out any extra.
• Sift the flour, baking soda, and baking powder into a large mixing bowl or bowl of a stand mixer fitted with a paddle attachment. Add sugars, salt, and spices to the same bowl, and mix on low for about 30 seconds until all ingredients are combined.
  2 Cups All-Purpose Flour, 1 Tbsp Baking Powder, 1 Tsp Baking Soda, 1 Cup Light or Dark Brown Sugar, ½ Cup Granulated Sugar, 1 ½ Tsp Fine Sea Salt or Table Salt, 2 Tsp Ground Cinnamon, ½ Ts Ground Allspice, ¼ Tsp Ground Ginger, ¼ Tsp Ground Nutmeg
• With the mixer on low, add butter 1 Tbsp at a time and let mix for about 30 seconds before adding the next Tbsp. Once the final Tbsp of butter is tossed in, continue mixing for 3 minutes or until the mixture looks uniformly like coarse sand and no large clumps remain.
  8 Tbsp Unsalted Butter
• Add each egg one at a time with the mixer on low until just combined. Add the vanilla and mix until combined. It will look like a thick dough.
  4 Large Eggs, 1 ½ Tsp Pure Vanilla Extract
• Peel, core, and purée the apple in a food processor (alternately, you can finely chop the apple and use a masher to achieve similar results; or you can use 1/3 cup of applesauce). Add the vegetable oil, milk, sour cream, and puréed apple into a liquid measuring cup and whisk with a fork to combine. Slowly stream the liquid ingredients into the dry ingredients with the mixer on low speed, ideally over 30 seconds to 1 minute, until almost combined and a few streaks of flour remain. Scrape the side of the bowl down.
  ¼ Cup + 2 Tbsp Vegetable Oil, ½ Cup Whole Milk, 1 Large Honeycrisp Apple, 1/4 Cup + 2 Tbsp Sour Cream
• Add the shredded carrots and nuts (if using) into the batter. Mix on low speed until just combined. Use a rubber spatula to finish gently folding the mixture if needed.
  5 Medium Carrots, 1 Cup Pecans or Walnuts
• Pour into the prepared cake pan, spread the batter out evenly, and bake on the center rack until:

  -The cake bounces back when you gently touch the center with your finger. (Important!!)

  -The edges of the cake are pulling away from the sides of the pans. 

  About 40-50 minutes. Place on a cooling rack, and cool completely before frosting.

Cream Cheese Frosting

• Add butter and cream cheese to a large mixing bowl or bowl of a stand mixer fitted with a paddle attachment. Beat on low speed until combined and creamy.
  8 Oz Cream Cheese, 4 Tbsp Unsalted Butter
• Add the powdered sugar in 3-4 batches, and mix until almost combined each time. Add the pinch of salt, vanilla, and milk and mix on medium speed until smooth. Adjust milk and powdered sugar to your desired consistency from there.
  3 ½ Cups Powdered Sugar, 1 ½ Tsp Pure Vanilla Extract, 1 Tbsp Milk or Cream, 1 Pinch Fine Sea Salt or Table Salt
• Frost the fully-cooled cake with an offset or rubber spatula. Pipe designs around the perimeter, if desired. Sprinkle candied pecans or walnuts over the top, and enjoy!
  ½ Cup Candied Pecans or Walnuts*