Peel and finely grate the carrots using the holes of a box grater.
Preheat your oven to 225°F.
Spread the pecans evenly on an unlined baking pan and roast them in the oven for 15-20 minutes. Remove from the oven and let cool.
Increase the oven temperature to 350°F.
On parchment paper, use a pencil to trace the bottom of the cake pans and cut the circles out. Spray the inside of the cake pans with non-stick cooking spray, add the traced circles to the pan with the pencil side down and spray with more non-stick spray.
In a medium bowl, sift the flour, baking powder, baking soda, salt, cinnamon, and ground nutmeg.
In a large bowl, whisk both sugars with the vegetable oil, add the room temperature eggs, vanilla extract, and sour cream. Whisk until smooth. Add the dry ingredients and whisk until smooth. Stir in the chopped pecans and grated carrots.
Pour the cake batter evenly into the prepared cake pans. Bake for 20-22 minutes. A toothpick inserted into the center of the cake should come out clean.
Let the cakes cool for 5-10 minutes before removing them from the pans. Use a butter knife to separate the cake from the edge of the pan and then flip the pan over to remove the cake. Keep the cake sitting upright because the tops of the cake will stick to any surface. Let the cakes cool completely before frosting. You can also leave the cakes in the pans, cover them with aluminum foil, and then place the pans in the freezer overnight, which makes frosting easier.