Preheat your oven to 375 degrees F and spray a springform pan with non-stick spray (preferably 9-10 inches).
In a large bowl, whisk together the flour, baking soda, ground cinnamon, nutmeg, cloves, allspice and salt. Set aside.
In the bowl of your stand mixer, with paddle attachment fixed, cream together the sugars and oil until smooth and creamy. Add the sour cream and buttermilk and mix again to incorporate. Add each egg, one at a time, mixing after each addition. Add the vanilla extract and mix again.
Add the dry ingredients to the wet, and mix until just moistened. Do not overmix. Fold in the carrots and 1/2 cup of chopped pecans.
Pour the batter into the prepared pan and bake for 20-25 minutes or until a toothpick comes out clean. Remove from heat. Place the pan directly on a wire rack to cool completely.
While your cake is cooling, prepare your frosting.
In your stand mixer, with paddle attachment fixed, cream together the cream cheese and butter. Add the confectioner's sugar, in 1 cup increments until combined. Add more as needed. Add the milk, vanilla extract, cinnamon and salt. Mix again.
Frost the cake once it has cooled completely. Sprinkle with the remaining pecans and enjoy!
The carrot cake will store in an airtight container for 3-5 days.