Preheat oven to 350 degrees F (175 degrees C). Spray a 9x5-inch loaf pan with cooking spray.
Place sweet potato on a microwave-safe plate and pierce skin 5 or 6 times. Cook in the microwave, rotating halfway through, until tender, 5 to 8 minutes. Cool until easily handled, about 5 minutes. Peel and mash in a small bowl.
Mix whole wheat flour, baking soda, cinnamon, nutmeg, and salt together in a large bowl.
Whisk applesauce, eggs, and maple syrup together in a separate bowl. Mix in 1 cup mashed sweet potato.
Pour applesauce mixture over flour mixture; stir to combine. Fold in walnuts. Pour into the prepared loaf pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 55 minutes. Cool in the pan for 15 minutes; invert onto a wire rack and let cool completely, about 20 minutes.