Preheat the oven to 350 degrees F. Grease 2 8-inch baking pans. Set aside.
Whisk the flour, baking powder, baking soda, salt, and spices to combine. Set aside.
Line a plate with paper towels. Take the finely grated apples and dry them out on the paper towels, pressing the towels to absorb any excess liquid.
Combine the eggs, oil, granulated and light brown sugars, and the vanilla extract. To this wet mixture add the dry ingredients. Fold in the apples and walnuts.
Pour the batter into the prepared pans, tapping the pans on the counter to remove any air bubbles.
Bake the cake for 25 to 30 minutes, rotating half way.
Remove from the oven, let them rest in the pans for 10 minutes before removing them to cool completely.