Preheat the oven to 350ºF (180ºC).
Butter or spray a 3x8-inch (20x7cm) loaf cake pan. Add a strip of parchment paper that covers the bottom and up the two narrow sides. The long sides will be left unlined. The paper will help you remove the cake more easily after it's baked.
Wash and dry 2 apples (skin and all) and process them until chopped but not pureed. You can also very finely chop them by hand, or grate them with a large-holed grater. They will begin to release liquid, which is fine; we want that.
Stir the dry ingredients in a large bowl: 1 cup all-purpose flour, ½ cup whole wheat flour, 1 cup sugar, ¼ teaspoon baking soda (sift it to avoid clumps) and ¼ teaspoon salt and ½ teaspoon ground cinnamon.
Add the wet ingredients in the middle: ½ cup vegetable oil , 2 eggs, 1 teaspoon vanilla extract , and ½ teaspoon orange zest. Mix well by hand or with an electric mixer.
Fold in the apples, chopped ½ cup walnuts, and mix. The batter will become wetter and easier to stir.
Pour into the prepared pan and bake for 40 minutes, or until a tester comes out dry. Sometimes it takes more. If it's browning too quickly cover the top loosely with a piece of aluminum paper while it keeps baking.
Let cool for about 20 minutes. Run a smooth blade knife around the edges to loosen first and unmold carefully. Let cool completely on a wire rack and glaze.
Keep well wrapped for no more than 1 day at room temperature and in the fridge a few more days. It can be frozen, well wrapped in film and aluminum foil, before glazing.