Line a 9- by 5-inch loaf pan with waxed or parchment paper (or grease and flour it), then set it aside. Heat the oven to 350°.
Combine the applesauce, sugar, brown sugar, eggs, oil, yogurt, and vanilla extract in a large bowl. Whisk well to blend.
In another large bowl, combine the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Make a well in the dry ingredients with a wooden spoon and pour in the applesauce mixture. Stir just enough to combine; do not overmix. Fold in the apples and walnuts.
4. Scrape the batter into the prepared pan and smooth the top with a spoon. Evenly sprinkle one tablespoon of sugar over the top. Bake on the center oven rack until a toothpick inserted into the center of the bread comes out clean, about 50 to 55 minutes.
5. Remove the pan from the oven and put it on a cooling rack for about 15 minutes, then remove the loaf from the pan and place it on the rack to finish cooling. Makes 10 servings.