Adjust oven rack to middle position; heat oven to 350 degrees. Grease (really well) a 13 by 9-inch baking pan or two 9-inch round pans.

Whisk together flour, baking powder, baking soda, cinnamon, nutmeg, cloves and salt in large bowl; set aside. In a food processor (or by hand like I did), shred carrots finely (you should have about 3 cups); transfer carrots to bowl and set aside.

In bowl of standing mixer fitted with paddle attachment (or in large bowl and using hand-held mixer), beat granulated and brown sugars and eggs on medium-high until thoroughly combined. Reduce speed to medium; with mixer running, add oil in slow, steady stream, being careful to pour oil against inside of bowl (if oil begins to splatter, reduce speed to low until oil is incorporated, then resume adding oil). Increase speed to high and mix until mixture is light in color and well emulsified, about 45 seconds to 1 minute longer. Turn off mixer and stir in carrots, dry ingredients, and nuts by hand until incorporated and no streaks of flour remain.

Pour into prepared pan(s) and bake just until toothpick or skewer inserted into center of cake comes out clean, about 30-35 minutes (for two round cake pans-you may need to cook it longer for one 9"x13" pan). Every oven varies, so check it regularly so you don't over-bake it. Cool cake in pan on wire rack for about 20 minutes, then carefully remove to cooling racks to cool completely.

When cake is cool, mix cream cheese, butter, vanilla, and powdered sugar at medium high speed in clean bowl of standing mixer fitted with whisk attachment (or in large bowl using handheld mixer) until well combined, about 30 seconds, scraping down bowl with rubber spatula as needed. Frost, decorate with nuts or extra frosting and eat!