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heat the oil in a medium pot over medium heat.
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add the sausage and cook, breaking the meat up with a wooden spoon, until browned, about 4 minutes.
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add the onions and celery and continue to cook, stirring, until the vegetables are softened, about 5 minutes.
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add the beans, tomatoes, broth and 4 cups water and increase the heat to medium-high to bring to a simmer.
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continue to simmer, adjusting the heat if necessary, until the vegetables are tender, about 10 minutes.
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add the tortellini and continue to cook until they are tender, 3-5 minutes.
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season to taste with salt and pepper.
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serve in bowls topped with a spoonful of pesto and a sprinkle of grated parmesan.