Preheat oven to 350°F. Grease two 9-inch round cake pans. Line the bottoms with parchment paper and grease the paper. Set aside.
Mix the wet ingredients: 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 teaspoons vanilla extract
Add the dry ingredients: Add flour, baking powder, baking soda, cinnamon, and nutmeg. Mix until just combined and only a few streaks of dry ingredients remain. Fold in the carrots and prepared pecans, and pour into the prepared cake pans.
2 ½ cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1 ½ teaspoons ground cinnamon, ¼ teaspoon ground nutmeg, 3 cups grated carrots, 1 cup toasted pecans
Bake in the preheated 350°F oven until a skewer inserted into the middle of the cake comes out clean, 35-45 minutes. Remove from the oven and cool in the pans for 10 minutes. Then remove from the pans and cool completely before frosting.
Make the frosting: While the cake is cooling, in the bowl of an electric mixer, beat the cream cheese on medium speed 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. 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.
Assemble: 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 chills in the refrigerator for up to 2 hours before frosting the cake.