Preheat oven to 350°F. Butter a 9x5-inch loaf pan and line with parchment paper, if desired.
In a bowl, combine applesauce, ½ cup of sugar, brown sugar, eggs, oil, yogurt, and vanilla in a bowl. Whisk to blend.
In a separate bowl, sift together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Make a well and add applesauce mixture. Stir until combined. Fold in diced apples and walnuts. Scrape batter into prepared pan and smooth the top. Sprinkle with the remaining tablespoon of sugar.
Bake on the center oven rack for 50 to 55 minutes, or until a tester inserted into the center comes out clean.
Transfer to a cooling rack for 10 minutes. Turn the bread out of the pan and cool thoroughly before slicing.