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1
Adjust an oven rack to the middle position and heat the oven to 350 degrees.
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2
Lightly coat a 13 by 9-inch metal baking pan with vegetable oil spray, then line the bottom with parchment paper.
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3
Whisk the flour, baking powder, baking soda, spices, and salt together in a medium bowl; set aside.
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4
Using an electric mixer, beat the eggs and sugars together in a medium bowl until they turn thick and creamy, 1 to 3 minutes.
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5
Turn the mixer to low and slowly whip in the oil until thoroughly combined and emulsified, 30 to 60 seconds.
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6
Sift half the flour mixture over the batter and gently mix inches Repeat once more with the remaining flour mixture and continue to whisk the batter gently until most of the lumps are gone (do not overmix).
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7
Using a rubber spatula, gently stir in the carrots.
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8
Pour the batter into the prepared pan, and smooth the top.
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9
Bake until a toothpick inserted into the center of the cake comes out with a few moist crumbs attached, 35 to 40 minutes, rotating the pan halfway through baking (do not overbake).
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10
Cool the cake in the pan for 10 minutes, then invert the cake onto a wire rack and remove the parchment paper.
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11
Flip the cake right-side up, and cool completely on a wire rack, about 2 hours, before frosting (if desired) and serving.
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12
Mix the cream cheese and vanilla together in a large bowl with a rubber spatula.
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13
Add the confectioners sugar and stir until thoroughly combined and smooth.
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14
Frost the top of the cake.
