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Use the tip of a knife to slice down the length of the sausages. Peel off the casing and discard.
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Heat a large pot over medium heat. Once the pot is hot, add oil and swirl to coat the bottom. Add pork and break apart with a spoon. Cook, stirring occasionally, until browned and crumbly, 6-8 minutes.
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Add garlic and onion to the pot and cook, stirring frequently, until softened, 4-5 minutes.
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Add beans, broth, and spices to the pot. Cover and bring to a simmer.
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Add potatoes and kale to the pot.
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Let the soup simmer, covered, until potatoes are fork tender, 10-15 minutes.
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Add cream and stir to combine.