Preheat your oven to 350°F (175°C).

Grease a 9x13 inch baking pan with butter or non-stick spray.

In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.

In another bowl, combine the granulated sugar, brown sugar, oil, eggs, and vanilla. Whisk until smooth and well blended.

Gradually add the wet mixture to the dry ingredients, stirring until just combined.

Gently fold in the diced apples and nuts, if using.

Pour the batter into the prepared baking pan, smoothing the top with a spatula.

Bake in the preheated oven for 50 minutes or until a toothpick inserted in the center comes out clean.

Let the cake cool in the pan for at least 10 minutes before transferring it to a wire rack.