If using fresh pumpkin or squash, preheat oven to 425°F. Peel, seed and chop pumpkin or squash, coat with EVOO, salt and pepper, and roast to tender, 45 minutes. If using canned pumpkin purée, skip this step.
Heat 1 tablespoon EVOO in a soup pot over medium-high heat. Sauté carrots and onions to tender, about 10 minutes. Season with nutmeg, cinnamon, coriander, cumin, paprika, a drizzle of honey, salt and pepper to taste. Toast spices, about 1 minute.
Add the carrots and onions along with the roasted pumpkin or squash to the bowl of a food processor and purée with a splash of stock. If using canned pumpkin, purée the onions and carrots together with some stock and stir in the canned pumpkin to combine.