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1
Heat the oven to 350 degrees F and arrange a rack in the middle.
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2
Place the flour, baking powder, baking soda, cinnamon, nutmeg, allspice, and salt in a large bowl and whisk to aerate and break up any lumps; set aside.
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3
Place the eggs, sugars, oil, and yogurt in a large bowl and whisk until the eggs are broken up and the mixture is thoroughly combined.
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4
Using a rubber spatula, fold in the flour mixture until just combined.
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5
Stir in the carrots until evenly mixed.
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6
Pour the batter into a 13-by-9-inch glass baking dish (no need to coat with butter), smoothing it into the corners with the rubber spatula.
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7
Bake, rotating the dish after 20 minutes, until a toothpick or cake tester inserted in the center comes out dry with just a few crumbs, about 40 to 50 minutes total.
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8
Transfer to a wire rack to cool completely before frosting, at least 2 hours.
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9
Meanwhile, toast the nuts.
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10
Place the nuts on a baking sheet and bake until lightly browned and fragrant, about 10 minutes.
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11
Transfer the nuts to a cutting board to cool slightly, coarsely chop them, and set aside.
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12
Place the butter and cream cheese in the bowl of a stand mixer fitted with a paddle attachment and beat on medium-high speed until light, fluffy, and fully incorporated, about 3 minutes.
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13
Stop the mixer and scrape down the sides of the bowl and the paddle with a rubber spatula.
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14
Add the powdered sugar and vanilla.
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15
Turn the mixer to low and mix until the sugar is incorporated, about 30 seconds.
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16
Stop the mixer and scrape down the sides of the bowl and the paddle again.
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17
Turn the mixer to medium-high speed and mix until the frosting is creamy and fluffy, about 3 minutes.
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18
Spread all of the frosting in an even layer over the cooled cake and evenly sprinkle the toasted nuts over the frosting.
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19
If you dont plan to eat the cake within 4 hours, cover it with plastic wrap and refrigerate for up to 3 days.
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20
Before serving, let the cake sit at room temperature for about 45 minutes to take the chill off.