FOR THE CAKE: Adjust oven rack to middle position, heat ove to 350 degrees. Spray 13 x 9-inch baking pan with nonstick cooking spray. Line bottom of pan with parchment and spray parchment.
Whisk together flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt in large bowl; set aside.
In a food processor fitted with large shredding disk, shred carrots (you should have about 3 cups); transfer carrots to bowl and set aside. Wipe out food processor borkbowl and fit with metal blade. Process granulated and brown sugars and eggs unml frothy and throughtly combined, about 20 seconds. With machine running,add oil though feed tube in steady stream. Process unil mixture is light in color and well emulsified, about 20 seconds longer. Scrape mixture into medium bowl. Stir in carrots and dry ingredients unil incorpated and no streakes of flour remain. Pour into prepared pan and bake until a toothpick skewer inserted into center of cake comes out clean, 35 to 40 minutes, rotating pan halfway through baking time. Cool cake to room temperature in pan on wire rack, about 2 hours.
FOR THE FROSTING: When cake is cool, process cream cheese, butter, sour cream, and vanilla in clean food prcesser workbowl until combined about 5 seconds, scraping down bowl with rubber spatula as needed. Add confectioners' sugar and process until smooth, about 10 seconds.
Run paring knife around edge of cake to loosen from pan. Invert cake onto wire rack, peel off parchment, thn invert again onto serving platter. Using icing spatula, spread frosting evenly over surface of cake. Cut into squares and serve. (Cover leftovers and refrigerate for up to 3 days.)
SPICED CARROT CAKE WITH VANILLA BEAN-CREAM CHEESE FROSTING (Inspired by Chai tea)
VARIATION: Follow recipe for Simple Carrot Cake with Cream Cheese Frosting, substituting equal amount ground black pepper for nutmeg, increasing cloves to 1/4 teaspoon, and adding 1 tablespoon ground cardamon along with spices. For Frosting, using paring knife, halve and scape seeds from 2 vanilla beans and add seeds to food processor along with vanilla extract.