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Pierce sweet potatoes several times with a sharp knife and bake in a 350°F oven 1 hour or until tender.
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When cool enough to handle, peel, place in a large bowl and mash with a fork or potato masher.
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Heat oil in a medium saucepan over medium heat. Add onion, celery, garlic and basil.
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Cook, stirring frequently, 10 minutes or until vegetables are tender.
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Add small amounts of water as necessary, about a tablespoon at a time to prevent sticking.
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Gradually sit milk into saucepan. Add mashed sweet potatoes, salt, pepper, and allspice.
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Cook, stirring frequently, until soup just begins to boil.
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Serve right away or remove from heat and cover until serving time.