Preheat oven to 350°F (175°C). Grease and line two round cake pans with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, brown sugar, baking soda, baking powder, salt, cinnamon, and nutmeg until evenly combined.
In a separate bowl, whisk together the vegetable oil, eggs, vanilla extract, and buttermilk until smooth.
Pour the wet ingredients into the dry ingredients. Gently mix until just combined. Do not overmix.
Finely chop the shredded carrots again so they are small and soft. Fold them into the batter using a spatula.
Divide batter evenly between prepared pans and smooth the tops.
Bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean.
Cool cakes in pans for 10 minutes, then transfer to a wire rack to cool completely before frosting.