Preheat oven to 350 degrees with the trays in the upper and lower third. Line 2 cupcake cans with paper liners.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, cloves and salt. Set aside.
In stand mixer (or do by hand in a large mixing bowl), whisk together the eggs, granulated sugar and brown sugar for about 1 minute. Slowly drizzle in the vegetable and whisk for another 1 minute until emulsified. Mix in carrots and whisk for 20 seconds. Add in the dry ingredients in 2 batches and mix until just combined and no streaks of flour remain.
Fill the cupcake liners 3/4 full. Bake until the cupcakes are set and a wooden skewer comes out clean, about 30 minutes, rotating the pans halfway thru. Remove and allow to cool completely before frosting. There will be enough batter remaining to make 4 more cupcakes if you wish to use all the batter.
Make the frosting by whisking together the cream cheese, butter, sour cream, vanilla and powdered sugar. Transfer to a plastic bag, snip the end off, and pipe the frosting onto the cupcakes.
Will keep in an airtight container for 4 days. The cupcakes freeze wonderfully. Just transfer to an airtight container before frosting. Freeze up to 6 months. Allow to thaw in the fridge for about 12 hours, then frost them.