Preheat the oven to 350°F. Lightly grease two standard muffin pan or cupcake pans; or line the pans with papers and grease the papers. Note: To make a loaf and cupcakes instead of 2 dozen cupcakes, see “tips,” below.
To Make the Cupcakes
In a large bowl or the bowl of your stand mixer, beat together the oil, sugar, salt, eggs, and spices.
Whisk the flour with the baking powder and baking soda and add to the bowl, stirring to combine.
Add the carrots and nuts and mix until just blended. Scoop the batter into the prepared pans, using about 55g for each cupcake; a muffin scoop works well here.
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.
Remove the cupcakes from the oven, and after about 10 minutes transfer them to a rack to cool. Allow them to cool completely before frosting.
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.
Reduce the speed to low and add the powdered sugar, vanilla, and spices.
Return to medium speed and beat for 1 to 2 minutes, until creamy.
To Make the Topping
Line a baking sheet with parchment and set aside.
In a small saucepan, combine the sugar and water and cook over medium-high heat until the mixture reaches 320°F. Do not stir.
Remove the syrup from the heat and add the walnuts.
Carefully transfer the mixture to the prepared pan. Cool completely before breaking into small pieces.
Frost the cupcakes and garnish with the walnut brittle topping before serving.
Store, covered, in the refrigerator for up to one week; freeze for longer storage.
To make a loaf + cupcakes: Lightly grease a tea loaf pan (or 9” x 5” loaf pan) and one standard muffin or cupcake pan. Prepare the batter as directed and spoon 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 or cupcake pan. (You’ll make about six cupcakes if you’ve used a tea loaf pan, eight cupcakes if you’ve used a 9” x 5” pan.) Bake the tea loaf for 45 to 50 minutes; or the 9” x 5” loaf for 65 to 75 minutes, tenting after 45 minutes if the top is getting too dark.Bake the cupcakes as directed above.Cool, frost with the cream cheese frosting, and garnish with the walnut brittle.
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