Preheat oven to 350°F.
Butter and flour a 9-inch round, 3-inch deep cake pan.
Line the bottom with parchment paper and set aside.
Grate the carrots on a medium grate.
Put the grated carrots into a bowl and set aside.
In the bowl of the food processor combine the sugar, brown sugar, eggs, and yogurt.
With the processor running drizzle in the vegetable oil.
Whisk the flour, baking powder, baking soda, spices, and salt together.
Add to the food processor and pulse until blended, about 5 seconds.
Add the carrots and pulse just until blended.
Pour the batter into the cake pan.
Bake on the middle rack of the oven for 45 minutes.
Reduce the heat to 325°F and bake for another 20 minutes or until a cake tester comes out clean.
Remove the pan from the oven and allow the Carrot Cake to cool 15 minutes in the pan. After 15 minutes, turn the cake out onto a platter and let it cool completely.
Frost with cream cheese frosting after the Carrot Cake has cooled completely.