In a baking dish toss squash with spices, salt and 6 T olive oil. Roast at 400°F for 12 minutes.
In a large pot over medium-high heat, cook onions and garlic in remaining 2 T oil until tender. Add squash and cook 5 minutes. Add broth and simmer 30 minute. Turn off heat and cool 10 minutes.
Blend soup with Chobani in 3 batches. Re-warm and serve.