Preheat the oven to 350° F (175° C) and line a 12-cup muffin pan with muffin cups. Peel and slice the carrots, then chop them in a food processor on high until they are finely chopped, but not mushy. Set the carrots aside.
In a medium bowl, add the flour, baking powder, baking soda, salt, cinnamon, nutmeg and cloves. Stir until they are fully combined, then set aside.
In a large bowl, add the sugar and eggs. Using an electric mixer fitted with a whisk attachment, beat at medium-high speed until the mixture is pale yellow and slightly thickened, about 1-2 minutes.
Add the vanilla, oil, and chopped carrots, and mix at medium-low speed until well combined, about 30 seconds.
Sift in ⅓ of the flour mixture and mix on low until just combined, about 20-30 seconds. Scrape the edges of the bowl and add another third, and then repeat until all of the flour is incorporated.
Spoon or ladle the batter into the 12 muffin cups. The cups should be around ¾ to ⅞ full.
Bake for 22-24 minutes, or until a toothpick or or chopstick inserted in the center of a cupcake comes out clean.
After 10-15 minutes, remove the cupcakes from the pan to cool. Let them cool for a total of 30-45 minutes before frosting.