Preheat oven to 350 degrees F. Line two standard 12-cup muffin tins with paper liners and set aside.

In a medium bowl, add the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves. Whisk together to combine and set aside.

Wash carrots well (no need to peel them) and in a food processor fitted with a fine shredding disk (or grate by hand using a fine grater), shred the carrots. You should have about 1 ¾ cups of packed carrots. Set aside.

In a large bowl using a hand-held mixer (or use a stand mixer with the whisk attachment or by hand with a whisk), beat the granulated sugar, brown sugar, and eggs on medium-high speed until thoroughly combined, about 45 seconds.

Reduce the speed to medium and with the mixer running, add oil in a slow, steady stream, being careful to pour oil away from the beaters or whisk.

Increase the speed to high (or whisk quickly by hand) and mix until the batter is light in color and well emulsified, about 45 seconds to 1 minute longer.

Stir in the carrots and dry ingredients by hand until incorporated and no streaks of flour remain (being careful not to overmix).

Divide the batter evenly among the prepared muffin tins, filling the cups about ⅔ full. Bake until a toothpick or skewer inserted into the center of the cupcake comes out clean, about 20-23 minutes.

Let the cupcakes cool for about 10 minutes in the pan and then transfer them to a cooling rack to cool completely.

In a stand mixer fitted with the paddle or whisk attachment or in a large bowl using a handheld electric mixer, whip together the cream cheese, sour cream and granulated sugar for 1-2 minutes until creamy and smooth.

Add the vanilla and heavy cream and mix until light and fluffy, 1-2 minutes, scraping down the sides of the bowl as needed. Add additional heavy cream and whip thoroughly if needed for a softer frosting.

Frost the cooled cupcakes and store the frosted (or unfrosted) cupcakes in the refrigerator until serving.