Preheat the oven to 425°F. Cut the stem end off the squash, then cut the squash in half lengthwise. Scrape out the seeds and reserve. Brush the cut surface of the squash with olive oil, then sprinkle with salt and pepper. Arrange cut side down in a baking pan. Add about ½-inch water to the pan. Pierce the sweet potato several times with a fork and place on a small baking pan. Remove most of squash pulp from the squash seeds, then place the seeds in a pie pan or cake pan. Add 1 teaspoon of oil and a good sprinkling of salt and pepper; mix to coat.
Roast seeds until brown and crisp, stirring occasionally, about 10 minutes. Roast the squash and sweet potato until soft when pressed, 1 to 1½ hours, adding more water to the squash pan to maintain about ¼-inch, if necessary. Remove from the oven and let stand until cool enough to handle.
Meanwhile, heat 2 tablespoons oil in a heavy large pot over medium heat. Add the onions and sauté until starting to brown on the edges, about 12 minutes. Add the mushrooms, sprinkle with salt and pepper. Sauté until beginning to soften about 4 minutes. Add the paprika, 1 teaspoon Aleppo pepper and cinnamon and stir just until fragrant, about 30 seconds. Add 1½ quarts broth and bring to a boil.
Scrape the squash and sweet potato from their skins, reserving any liquid in the pan with squash. Add squash, sweet potato and any liquid in squash pan to the soup. Simmer until flavors blend and squash and sweet potato are incorporated, using a potato masher to break down the squash and sweet potato, about 25 minutes. Season to taste with salt and pepper. For a smoother texture, use an immersion blender to partially puree the soup, leaving some texture. Thin to desired consistency with more broth. (Can be prepared 3 days ahead. Cover and refrigerate. Rewarm over medium heat, thinning with more broth if desired).
Ladle the soup into bowls. Sprinkle with roasted squash seeds, Aleppo pepper, and thyme. Drizzle with maple syrup and serve.