Preheat the oven to 350 degrees F. Line two 9-inch round cake pans with parchment and lightly coat with cooking spray. Spread the walnuts out on a rimmed baking sheet and toast until light brown and fragrant, about 7 minutes.
Whisk together the flour, baking powder, apple pie spice and salt in a medium bowl and set aside. Whisk together the granulated sugar and eggs in a large bowl until smooth, about 1 minute. Whisk in the oil until well combined. Add the grated carrots, vanilla and walnuts and mix well. Add the flour mixture and stir until just combined. Divide the batter evenly between the prepared pans.
Bake until the cakes are nicely browned and a toothpick inserted in the center comes out clean, about 30 minutes. Cool in the pans on a wire rack for 10 minutes. Loosen the edges with a spatula, turn the cakes out and let cool completely on the rack, right-side up, about 2 hours.
For the frosting:
Beat the cream cheese and butter with an electric mixer on medium-high speed in a large bowl, scraping down the sides of the bowl occasionally, until smooth, about 2 minutes. Add the confectioners' sugar, vanilla and salt, gradually increase the mixer speed to medium high and beat until the frosting is fluffy and smooth, about 3 minutes. With the mixer running on medium-high speed, slowly pour in the cream and beat until it's all incorporated. Continue beating until the frosting is slightly lighter in color and creamy, about 1 minute more.
Remove the parchment from the cake layers. Place one of the cake layers on a serving plate and spread 1 cup of the frosting evenly over the top, almost to the edge. Top with the other cake layer and use the remaining frosting to frost the top and sides of the cake.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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