Heat your oven to 425°F. Coat a large baking sheet with the olive oil and add all the vegetables, with the squash pieces skin side up.
Roast for 30 minutes, flip the vegetables with a spatula, and roast for another 20 minutes.
Once the vegetables are cool enough to handle, scrape all the squash flesh from its skin and transfer to your food processor along with the carrots, onions, 1 cup of the broth, and the spices.
Pulse a few times, adding more liquid as needed until it reaches a purée consistency.
Taste and add more cinnamon and/or nutmeg as desired.