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Preheat oven to 350 degrees F. Coat a 9-by-5-inch loaf pan with baking spray.
Stir granulated sugar, yogurt and eggs together in a large bowl until well combined. Add applesauce, vanilla and 6 tablespoons melted butter; stir well to combine and set aside.
Whisk 1 cup all-purpose flour, whole-wheat flour, baking soda, apple pie spice and salt in a medium bowl. Add chopped apple and stir until the pieces are evenly coated. Add the flour-apple mixture to the egg mixture; stir until just combined. Spoon into the prepared loaf pan.
Combine walnuts, brown sugar, cinnamon and the remaining 1 tablespoon each melted butter and all-purpose flour in a small bowl. Sprinkle evenly on the batter in the pan.
Bake until a wooden pick inserted in the center of the loaf comes out clean, 55 to 60 minutes. Cool in the pan for 10 minutes. Gently turn out onto a wire rack; let cool completely, about 1 hour.