Preheat oven to 400 degrees. Line muffin pans with paper liners.
Beat the sugar, oil, and eggs together in bowl of electric mixer fitted with paddle attachment until light yellow. Add vanilla. In another bowl, sift together 2 cups flour, the cinnamon, baking soda, and salt.
Add dry ingredients to the wet ingredients. Toss the carrots, raisins, and walnuts with 1 tablespoon flour. Add to the batter and mix well.
Scoop batter into the muffin cups until each is almost full. Bake for 10 minutes, then lower the oven to 350 degrees F and bake for 35 minutes, or until a toothpick comes out clean. Let cool on a wire rack.
For frosting, mix cream cheese, butter, and vanilla in bowl of electric mixer fitted with paddle attachment until combined. Add confectioner's sugar; mix until smooth.
For the decoration, melt the butter in a skillet over medium heat; add the carrots and maple syrup and saute for 2 to 3 minutes, until carrots are tender. Spread them on a paper towel to cool.
When cupcakes are cool, frost them generously and garnish with big pinches of sauteed carrots. Makes 22 cupcakes.