Arrange wedges on baking sheet. Drizzle with olive oil, and sprinkle with sea salt and chili powder. Cover with foil. Roast 40 minutes, then remove foil and continue roasting until wedges are fork tender with golden edges, 20 - 30 minutes longer. Set aside to cool, then scoop the flesh from the skins and lightly mash.
Set a 4-quart dutch oven over medium heat. Add the olive oil, and then add the ginger, garlic, shallot, cumin, and a pinch of sea salt. Sauté until golden and fragrant, 5 - 7 minutes.
Add the garlic and chili powder, along with the roasted squash puree and vegetable stock. Bring mixture to a gentle boil, and then turn heat down to a bubbly simmer and cook 20 minutes.
Working in batches in the blender or with an immersion blender, puree the soup until very smooth. Return to Dutch oven and set over low heat. The soup my bubble and pops at this point, so take care.
Taste the soup, and add sea salt, lemon juice, fish sauce or coconut aminos, and honey or maple syrup to taste; it might take a few passes to get the balance of flavors just right.