Transfer to a bowl using a slotted spoon. Add the squash, carrots, celery, onion, chicken broth, 2 1/2 cups water and 1/4 teaspoon salt to the pot.
Cover and bring to a simmer, then reduce the heat to low and continue simmering until the vegetables are tender, about 15 minutes.
Puree the soup in a blender in batches, then return to the pot along with the sausage. Season with salt and pepper.
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