Heat oven to 350 degrees F. Spread pecans in a single layer on an ungreased baking pan. Transfer to oven, and roast until toasted and brown, about 8 minutes. Give the pan a shake midway through roasting to make sure pecans roast evenly. Remove pan from oven, and let stand until completely cool. Finely chop pecans, and set aside. Line muffin tin with cupcake liners. Set aside. Using the smallest holes (less than 1/4-inch in diameter) of a box grater, grate the carrots to yield 1 3/4 cups. Place grated carrots, eggs, buttermilk, vanilla, sugar, vegetable oil, and ginger in a large bowl; whisk until well combined. In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon. Using a rubber spatula, fold the dry ingredients into carrot mixture until just combined. Fold in toasted pecans. Using a large metal spoon, fill each paper cupcake liner to the top. Bake until a cake tester comes out clean, 20 to 25 minutes, rotating the pan halfway through. Let cool in pan for 10 minutes, then remove to cooling rack to cool completely. Spread about 1/ 4 cup frosting on each cupcake, and serve. Store in an airtight container for up to 2 days.
Place the butter in the bowl of an electric mixer fitted with a paddle attachment, and beat on medium-high speed until fluffy, about 2 minutes. Add the cream cheese and confectioners' sugar; beat until well combined and fluffy, about 2 minutes more. Add the orange zest, ginger, and salt. Beat an additional 5 minutes.
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