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1
Preheat the oven to 350.
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2
Spray a 9-by-13-inch metal baking pan with vegetable spray.
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3
Line the pan with parchment paper and spray the paper.
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4
On a rimmed baking sheet, toast the walnuts for about 7 minutes, until lightly browned and fragrant.
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5
Remove from the oven, add the butter and toss to coat the walnuts.
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6
In a medium bowl, combine the all-purpose flour, cake flour, baking powder, baking soda, salt, cinnamon, nutmeg, allspice and ginger; whisk to blend.
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7
In another bowl, whisk the eggs with the oil, granulated sugar, brown sugar and vanilla until smooth.
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8
Stir in the dry ingredients just incorporated, then stir in the carrots and walnuts.
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9
Pour the batter into the prepared pan and bake for 40 minutes, or until a tester inserted in the center of the cake comes out clean.
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10
Transfer the cake to a rack and let cool for 15 minutes.
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11
With a paring knife, loosen the cake from the side of the pan.
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12
Invert the cake onto the rack and gently peel off the parchment paper.
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13
Let cool completely, at least 2 hours.
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14
In the bowl of a stand mixer fitted with the paddle, beat the cream cheese with the butter at medium speed until blended, about 30 seconds.
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15
Beat in the confectioners' sugar in two batches, mixing thoroughly between additions, about 1 minute.
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16
Beat in the vanilla.
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17
Transfer the cake to a platter and spread the frosting over the top and sides.
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18
Serve at room temperature or chilled.
