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  1. Preheat the oven to 350°F. Lightly grease two standard muffin pans or cupcake pans. Or line with papers, and grease the papers.

  2. To make the cupcakes: Beat together the oil, sugar, salt, eggs, and spices.

  3. Mix the flour with the baking powder and baking soda, and stir in.

  4. Add the carrots and nuts, and mix until just blended. Pour into the prepared pans.

  5. 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 cakes from the oven, and after about 10 minutes transfer them to a rack to cool. Allow them to cool completely before frosting.

  6. To make the frosting: Beat the butter and cream cheese together until smooth.

  7. Beat in the salt and vanilla, then the sugar. Add a teaspoon of milk or cream if the frosting is too stiff to spread; add additional sugar if it's too thin.

  8. Frost the cupcakes, using a piping bag and tip for an elegant presentation.