Peel, trim and finely grate fresh carrots. I use my food processor to finely chop the carrots. You should have about 3 cups of finely chopped or shredded carrots.
Preheat oven to 350°F (170°C). Line a regular muffin pan with paper cupcake liners.
In a medium-size bowl, stir together flours, baking soda, baking powder, salt, cinnamon, cloves and nutmeg and set aside.
Beat together oil, brown sugar and granulated sugar. Add eggs and beat until well-incorporated. With the mixer on low speed, beat in flour mixture just until blended. Stir in carrots (and nuts and raisins if you wish).
Fill cupcake liners ¾ with batter. Bake at 350°F (170°C) for 20-25 minutes, until cupcakes are lightly browned and a wooden toothpick inserted in center of a cupcake comes out clean. Cool in pans on wire rack for 10 minutes. Remove from cupcakes from the pans and allow to cool completely on a wire rack.
For the Cream Cheese Frosting, beat the butter in the bowl of a stand mixer on high speed until light and fluffy. Add the powdered sugar, one third at a time, and beat on high speed for several minutes until mixture is light and creamy. Scrape the bowl and repeat the process until all of the powdered sugar is well incorporated. Beat in vanilla. You should now have a very stiff buttercream. Add the cream cheese and beat on high for a couple of seconds to incorporate. Scrape bowl and beat on high again for a couple of seconds.
The frosting can now be spread on the cupcakes or chilled until it is firm enough to pipe. This amount is enough to generously frost 24-30 cupcakes.
Chill frosted cupcakes.
Notes
*Oil may be reduced to 1 cup plus one tablespoon (260 ml), brown sugar to one cup minus one tablespoon (200 g) and granulated sugar to ⅔ cup (130 g) with no detectable change in taste or texture.Cupcake recipe adapted from The Family Circle Cookbook. Cream Cheese Frosting recipe adapted from Eat and Feast,Sugar-Sweet and Herznah.