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1
Adjust oven rack to middle position and heat oven to 350 degrees. Grease 13 by 9-inch baking pan. Lightly flour pan.
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2
Whisk flour, baking powder, baking soda, and spices together in large bowl and set aside.
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3
Mixer method: Shred carrots on large holes of box grater or use food processor (you should have about 3 cups); transfer carrots to bowl and set aside. Using stand mixer fitted with paddle, beat granulated sugar, brown sugar, and eggs on medium-high speed until thoroughly combined, about 45 seconds. 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. Mix in carrots. Mix in flour-spice mixture by hand until incorporated and no streaks of flour remain. If you want nuts or raisins or both, mix them in by hand.
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4
Scrape batter into prepared pan, smooth top with rubber spatula, and gently tap pan on counter to release air bubbles. Bake cake until toothpick inserted in center comes out clean, 35 to 40 minutes, rotating pan halfway through baking. Let cake cool completely in pan on wire rack, about 2 hours.
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5
Mix cream cheese with sour cream, butter, sugar, and spices. Spread frosting evenly over cake and serve. Cake can be refrigerated for up to 3 days.
