Heat oil in large soup pot over medium-high heat. When hot but not smoking, add onion and garlic. Cook, uncovered, stirring every now and then, until onion is completely softened, one to two minutes. Add sausage and cook, breaking it apart with a spatula or spoon, until cooked through.
Add tomatoes, broth, sweet potatoes, cumin, and fennel. Bring to a boil, reduce to simmer and cook until sweet potatoes are almost done, about 10 minutes. Add squash and chickpeas and cook, uncovered, for 15-25 minutes more, until squash is fork-tender. Taste, adjust seasonings with salt and pepper and serve.