Preheat your oven to 350°F (175°C) and grease a 9x13-inch sheet pan.

In a large bowl, whisk together all-purpose flour, baking soda, baking powder, salt, ground cinnamon, and ground nutmeg.

In another bowl, whisk the eggs, vegetable oil, brown sugar, white sugar, and vanilla extract until well combined.

Gently stir the wet mixture into the dry ingredients until just combined; do not overmix.

Fold in the chopped apples until evenly dispersed in the batter.

Pour the batter into the prepared pan and bake for 30-35 minutes or until a toothpick comes out clean.

Allow the cake to cool in the pan before slicing and serving.