Beat the sugar, oil, and vanilla together in the bowl of an electric mixer fitted with a paddle attachment.
Add the eggs, 1 at a time.
In another bowl, sift together the flour, cinnamon, baking soda, and salt.
With the mixer on low speed, add 1/2 of the dry ingredients to the wet ingredients.
Add the grated carrots, raisins, and walnuts to the remaining flour, mix well, and add to the batter.
Mix until just combined.
Line muffin pans with paper liners.
Scoop the batter into 22 muffin cups until each is 3/4 full.
Bake at 400°F for 10 minutes then reduce oven temperature to 350°F and cook for a further 35 minutes (**see note at bottom), until a toothpick comes out clean.
Cool on a rack.
Cream the cream cheese, butter, and vanilla in the bowl of an electric mixer fitted with a paddle attachment.
Add the sugar and beat until smooth.
When the cupcakes are cool, frost them generously and serve.
**I don't need to cook these for the entire additional 35 minutes. After I lower the temperature to 350°F; I start checking the muffins at around 15 minutes. Just keep watching them until a toothpick inserted in center comes out clean.