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Preheat the oven to 350°F. Lightly grease a tea loaf pan (or 9” x 5” loaf pan) and one standard muffin or cupcake pan. If using cupcake papers, line the pan with 8 papers and grease the papers. Note: To skip the tea loaf and make 2 dozen cupcakes, see "tips," below.
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To make the cake batter: In a large bowl or the bowl of your stand mixer, beat together the oil, sugar, salt, eggs, and spices.
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Whisk the flour with the baking powder and baking soda and add to the bowl, stirring to combine.
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Add the carrots and nuts and mix until just blended.
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Spoon the batter into the loaf pan, filling it about three-quarters full (about 1168g batter for the tea loaf pan or 1084g for the 9” x 5” pan). Spoon the remainder of the batter into the muffin pan. (You’ll have enough batter for about six cupcakes if you’ve used a tea loaf pan, eight cupcakes if you’ve used a 9” x 5” pan.)
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Place the cupcakes and loaf on the middle rack of the oven. Bake the cupcakes for 21 to 24 minutes, or until a toothpick inserted into the center of one of the middle cupcakes comes out clean. Bake the tea loaf for 45 to 50 minutes; or the 9” x 5” loaf for 65 to 75 minutes, tenting with foil after 45 minutes if the top is browning too quickly.
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Remove the cakes from the oven, and after about 10 minutes transfer them to a rack to cool. Allow to cool completely before frosting.
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To make the frosting: In a large bowl, or the bowl of your stand mixer, beat the cream cheese and butter at medium speed until smooth and creamy.
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Reduce the speed to low and add the powdered sugar, vanilla, and spices.
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Return to medium speed and beat for 1 to 2 minutes, until creamy.
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To make the topping: Line a baking sheet with parchment and set aside.
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In a small saucepan, combine the sugar and water and cook over medium-high heat until the mixture reaches 320°F. Do not stir.
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Remove the syrup from the heat and add the walnuts.
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Carefully transfer the mixture to the prepared pan. Cool completely before breaking into small pieces.
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Frost the loaf and cupcakes; garnish with the walnut brittle topping before serving.
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Storage information: Store cake, securely covered, in the refrigerator for up to one week; freeze for longer storage.