Preheat oven to 350°. In a large bowl, whisk together dry ingredients. In a separate bowl, whisk together eggs, pumpkin, and applesauce. Stir into dry ingredients just until moistened. Fold in walnuts.
Pour into a greased 9x5-in. loaf pan. Bake until a toothpick inserted in center comes out clean, 65-70 minutes. Cool in pan 10 minutes before removing to a wire rack.