Preheat the oven to 350 degrees F. Line the bottom of three 8-inch cake pans with parchment paper cut into circles to fit the pans, then coat the pans with cooking spray.
Place the flour, granulated sugar, brown sugar, baking powder, baking soda, nutmeg and salt in a large bowl and stir to combine.
In a separate bowl, whisk together the eggs, vegetable oil, eggnog and vanilla.
Slowly mix the wet ingredients into the dry ingredients until the mixture is just combined. Be careful not to overmix your batter.
Pour the batter evenly between the three pans. I recommend using a kitchen scale to make sure each pan has the same amount of batter.
Bake for 20-25 minutes, or until the cake is light golden brown and a toothpick comes out clean or with a few crumbs attached.
Let the cakes cool in the pans for 10 minutes, then carefully invert the cakes onto a cooling rack, and cool completely.