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Preheat oven to 375°.
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If using fresh pumpkin, remove stem and scrape out seeds and inner pulp. Cut each pumpkin into 3-4 sections and place on parchment lined baking sheet.
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Cut the top off of garlic bulb, so that the tops of cloves are exposed. Drizzle with 1 tablespoon of olive oil and wrap loosely in foil.
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Rub onion with ½ tablespoon of olive oil and place on a separate parchment lined baking sheet.
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Toss apple with remaining ½ tablespoon of olive oil and arrange in a single layer on baking sheet with onion.
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Place garlic, pumpkin (if using fresh), apple and onion into oven.
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Remove onion and apple from oven after about 20 minutes, when apple is soft and onion is lightly browned. Allow pumpkin and garlic to roast for another 15 minutes, until pumpkin is easily pierceable with a knife.
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If using fresh pumpkin, allow to sit until cool enough to handle. Gently peel off skin and transfer pulp to food processor bowl. Puree until smooth, stopping to scrape down sides of bowl as needed. If using canned pumpkin, simply place puree into food processor bowl.
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Add onion and apples to food processor bowl. Squeeze roasted garlic pulp from bulb. Place pulp in food processor bowl with pumpkin, onion and apple. Puree until smooth, stopping to scrape down sides of bowl as needed.
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Transfer pumpkin mixture to large saucepan. Add broth, soy milk, cinnamon, ginger, salt and pepper. Bring just to a simmer, stirring frequently. Remove from heat.