Position your oven rack in the middle of the oven and preheat oven to 325. Spray a 9x5 loaf pan with non stick spray. Set aside.
In a medium bowl, combine flour, cinnamon, baking powder, baking soda, salt, nutmeg and allspice and whisk until thoroughly combined. Set aside.
In another bowl or the bowl of an electric mixer, beat eggs on medium high for two minutes or until lightened in color. Add the brown sugar and beat for 2 minutes and then the granulated sugar and beat for 1 minute more. Scrape down sides as needed.
Drizzle in applesauce with beater on medium low. Reduce speed to low and add the pumpkin puree. Mix until thoroughly combined. Add the dry ingredients in two additions and blend for 10-15 seconds just until incorporated.
Spoon the batter into your prepared loaf pan and bake for 60-65 minutes or until a toothpick inserted in the center comes out clean. Cool loaf in pan for 15 minutes. Remove to wire rack and cool COMPLETELY.