1 (8-ounce) package brick style cream cheese, softened to room temperature
½ cup (115 grams) unsalted butter, softened to room temperature
2 cups (240 grams) powdered sugar
1 teaspoon pure vanilla extract
To make the carrot cake:
Preheat oven to 350°F (177°C). Spray two 9-inch round cake pans well with non stick cooking spray (you can also line the bottom of each pan with parchment paper for easier removal) and set aside.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt until well combined. Set aside.
In a separate large mixing bowl, whisk together the oil, eggs, brown sugar, granulated sugar, applesauce, and vanilla extract until fully combined. Add the grated carrots into the wet ingredients and mix until well combined.
Pour the wet ingredients into the dry ingredients and mix with a whisk or rubber spatula until just combined, making sure not to over mix the batter.
Pour the cake batter evenly between both prepared cake pans. Bake at 350°F for 30-35 minutes or until the tops of the cakes are set and a toothpick inserted into the center of each one comes out clean. Remove from the oven, transfer to a wire rack, and allow to cool in the pans for about 20-25 minutes. Once the cakes have cooled, remove from the pans and return the cakes to the wire rack to finish cooling.
To make the cream cheese frosting:
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a hand-held mixer, beat the cream cheese until smooth. Add the butter and mix for about 30 seconds-1 minute until well combined and smooth. Add in the powdered sugar and vanilla extract and continue mixing until fully combined, scraping down the sides of the bowl as needed.
To assemble the cake:
Level the tops of each cake with a knife or cake leveler. Place one of the cakes on a cake stand, top with a little over 1/2 cup of the frosting, and smooth it out into one even layer. Place the other cake on top and use the remaining frosting to frost the top and sides of the cake. Top with pecans or other toppings of choice if desired.