Preheat oven to 350.
In a medium-sized bowl, combine flour, brown sugar, baking powder, baking soda, cinnamon, nutmeg, and walnuts. Mix well and set aside.
In a separate bowl, combine pumpkin puree, applesauce, oil, milk, and vanilla. Mix well and pour into dry ingredients. Stir until batter is moist. Fold in chopped apple.
Pour into a greased and lightly floured 9 x 5 loaf pan. Bake for 40 to 45 minutes until a toothpick comes out clean and top is golden brown.