Preheat the oven to 350 degrees F and lightly coat an 8x4-inch loaf pan with baking spray. Set it aside.
Spread the walnut halves in a single layer on an ungreased baking sheet. Bake in the preheated oven for about 8 to 12 minutes, or until they are toasted and fragrant. Stir them once throughout the baking process. Be careful not to leave them unattended, as nuts can burn quickly. Transfer the toasted walnuts to a cutting board and roughly chop them. Set them aside.
In a large mixing bowl, combine the white whole wheat flour, baking soda, cinnamon, and salt.
In a separate bowl, whisk together the applesauce, canola oil, milk, sugar, egg, and vanilla until the mixture is smooth.
Create a well in the center of the dry ingredients and add the wet ingredients all at once. Mix them in by hand just until they are combined. The batter will be thick and stiff.
Fold in the diced apples and chopped walnuts. The batter will be thick, so gently and firmly use a rubber spatula to distribute the apples and walnuts evenly.
Pour the batter into the prepared loaf pan. Use the back of a rubber spatula to press and smooth the top so that it is mostly flat. If desired, prepare the cinnamon sugar topping by stirring the cinnamon and coarse sugar together in a small bowl. Sprinkle this mixture evenly over the top of the batter.
Bake the loaf for 25 minutes, then loosely tent it with foil and bake for an additional 20 minutes, or until a toothpick inserted into the center comes out clean without any wet batter clinging to it. Place the loaf pan on a wire rack and let it cool for 10 minutes, then remove the loaf from the pan and allow it to cool completely on the wire rack. Enjoy the bread warm or at room temperature.