Preheat oven to 400°F. In a small bowl, whisk oil, maple syrup, tamari, and cayenne. Season with salt.
On a rimmed baking sheet, toss squash, carrots, shallots, and garlic with maple mixture. Arrange in an even layer. Roast, flipping once, until vegetables are very tender and caramelized in places, 40 to 45 minutes.
Transfer vegetables to a large pot with any accumulated juices. Add stock, water, and ginger. Bring to a boil, then reduce heat and simmer, partially covered, 30 minutes. Let cool slightly.
Working in batches, transfer soup to a blender and puree until smooth (alternately, puree with an immersion blender.) If needed, add more hot water to thin out. Serve with fried shallots, yogurt, cilantro, and a squeeze of lime.