Prepare a 8.5 x 4.5 loaf pan - line with parchment paper, butter and flour the pan or spray with baking spray (whichever method works best for you). Set aside. Preheat the oven to 350°F / 177°C / Gas mark 4.
In a medium mixing bowl, whisk together flour, baking powder, baking soda, salt, 2 tsp. ground cinnamon, ground ginger, ground cloves, and ground allspice. Set aside.
In a separate mixing bowl, combine eggs, applesauce, sugars, vanilla, butter and cooked Hubbard squash. You can beat together with an electric mixer or whisk by hand. Just make sure they are well combined.
Pour wet ingredients into dry ingredients and using a rubber spatula stir and fold batter until combined (or use an electric mixer and beat for 2 - 3 minutes). A few small spots of flour is ok, make sure to scrape the bottom and sides of the bowl so no large pockets of flour remain.
Pour batter into prepared loaf pan and smooth the top with a spatula.
Mix remaining 1 tsp. cinnamon and 2 tbsp. raw sugar together, then sprinkle over the top of the batter.
Bake for 55 - 70 minutes, until a tester or skewer comes out clean, with a few moist crumbs attached.
Cool on a rack in the pan for 10 minutes, then turn the bread out and cool completely on a wire rack.
Video
Notes
Cooking the Hubbard squash ahead of time is a great timesaver. Do this the day before to save yourself having to bake it and wait for it to cool.