Grease two 9-inch round cake pans. Line bottoms with parchment paper and grease the paper. Set aside.
In the bowl of an electric mixer, combine the brown sugar, granulated sugar, eggs, oil, and vanilla extract. Mix on medium speed until combined, 3 minutes.
½ cup light brown sugar, 1 cup granulated sugar, 4 large eggs, 1 ¼ cups neutral oil, 1 ½ tsp vanilla extract
Add flour, baking powder, baking soda, cinnamon, and nutmeg. Mix until just combined and only a few streaks of dry ingredients remain. Fold in carrots and prepared pecans.
2 ½ cups all-purpose flour, 1 tsp baking powder, 1 tsp baking soda, 1 ½ tsp ground cinnamon, ¼ tsp ground nutmeg, 3 cups grated carrots, 1 cup toasted pecans
Pour into prepared cake pans and bake in preheated oven until a skewer inserted into the middle of the cake comes out clean, 35-45 minutes.
Remove from oven and cool in pans for 10 minutes. Then remove from the pans and cool completely before frosting.
For the frosting
While the cake is cooling, in the bowl of an electric mixture, mix the cream cheese on medium until smooth. Add in the butter and continue mixing until the cream cheese and butter are smooth and combined with no lumps, 3 minutes. The sides of the bowl may need to be scraped periodically while mixing.
8 oz cream cheese, 8 tbsp (1 stick) unsalted butter
Add the sour cream and mix to incorporate, 1 minute. Add the vanilla extract and powdered sugar. Mix on low until the sugar is incorporated and then mix on medium until smooth, 3-4 minutes.
Spread 1 cup of frosting on top of one 9-inch cake. Add the second cake and frost around the sides and top to cover the cakes. Serve immediately or store in the refrigerator to keep the frosting from getting too soft.
Video
Notes
I like to make the frosting while the cake cools and chill in the refrigerator for up to two hours before frosting the cake.