Heat 1 tablespoon olive oil in a large pot over medium-high heat. Add the sausage and cook, stirring occasionally, until browned, about 4 minutes. Transfer to a bowl using a slotted spoon. Add the squash, carrots, celery, onion, chicken broth, 2 1/2 cups water and 3/4 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 more minutes.
Puree the soup in a blender in batches, then return to the pot along with the sausage. Season with salt and pepper and keep warm.
Heat the remaining 1/3 cup olive oil in a small saucepan over medium-high heat. When the oil is very hot, add the sage leaves in batches and fry, turning, until dark green and crisp, about 1 minute. Remove with a slotted spoon and drain on paper towels. Ladle the soup into bowls and top with the fried sage.
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Photograph by Christopher Testani
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
Courtesy of Food Network Magazine
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