Preheat oven to 350 degrees F. Line a 12-cup muffin pan with cupcake liners and set aside.
In a large bowl, beat the sugars, eggs, oil, and vanilla with a hand mixer or even just by hand with a whisk. Stir in the freshly shredded carrots with a large spoon.
Add the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves, stirring until everything is combined. Don't overmix the batter.
Divide evenly between the 12 cupcake liners, filling each about 3/4 full.
Bake for 18-22 minutes, just until the tops of the cupcakes bounce back to the touch or a toothpick inserted into the center of a cupcake comes out clean with just a few crumbs. Cool completely before frosting.
Frosting
Beat softened cream cheese and butter in a medium bowl until light and creamy.
Add the powdered sugar and vanilla, mixing again just until combined and smooth. Don't overmix.
Transfer to a piping bag fitted with a decorative tip and frost the completely cooled cupcakes. Sprinkle with the chopped pecans for decoration and crunch.