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1
Make the cake: Position oven rack in the center of oven; preheat oven to 350u00b0; butter the bottom and sides of two 9-inch round cake pans; dust the pans with flour.
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2
Sift together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves in to a bowl.
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3
Whisk together the dry ingredients until blended; set aside.
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4
In the bowl of an electric mixer, using the paddle attachment, beat the eggs, sugar, and light brown sugar at medium speed until well combined, about 2 minutes.
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5
On low speed, add the oil, melted butter, milk, vanilla extract, ginger, and orange zest and mix until blended, scraping down the sides of the bowl with a rubber spatula as necessary.
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6
Add the flour mixture in three additions, mixing just until blended.
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7
Add the carrots and walnuts and mix until blended.
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8
Scrape the batter into the prepared pans, dividing it evenly.
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9
Bake the cakes for 25-30 minutes, until they are dark golden brown and a cake tester inserted into the center comes out clean.
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10
Cool the cakes in the pans on wire racks for 15 minutes.
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11
Invert the cakes onto the racks and cool completely.
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12
Make the frosting: melt the white chocolate in the top of a double boiler over barely simmering water, stirring frequently.
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13
Remove the chocolate from the heat and set aside to cool slightly.
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14
In the bowl of an electric mixer, using the paddle attachment, beat the cream cheese and butter at medium speed until smooth and creamy, about 1 minute.
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15
Add the melted white chocolate and mix until blended.
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16
Add the lemon juice, vanilla, and powdered sugar; mix until blended.
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17
Increase the speed to high and beat until smooth and creamy, about 1 minute.
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18
Use the frosting immediately, as it will begin to harden quickly.
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19
Frost the cake: place one of the cake layers right side up on a serving plate or cardboard cake round; spread the top of the cake with about 1 cup of frosting; top with the other cake layer, upside down.
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20
Frost the top and sides of the cake with the remaining frosting.
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21
Serve the cake immediately, or refrigerate; bring to room temperature before serving.