Preheat oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole dish lightly with cooking spray.
Sift flour, baking soda, cinnamon, nutmeg, and salt into a large bowl. Whisk in sugar, oil, eggs, and vanilla extract. Fold in apples and walnuts. Spread batter in the prepared casserole dish.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 40 to 45 minutes.
