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Do your prep: dice the onion, mince the garlic and jalapeno, and slice the squash and sausage.
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Heat a medium to large pot or dutch oven over medium-high heat. When hot, add the olive oil and when the oil is shimmering but not smoking, add the sausage slices and cook until they brown, 3-5 minutes. Add the onion and reduce the heat to medium, cooking until the onions become translucent, about 5-6 minutes. Add garlic and jalapeno and cook another minute or two. Add the squash and allow to brown slightly. Add chicken broth and tomatoes, and stir to combine.
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Bring mixture to a gentle boil, then reduce to medium-low. Season with salt, pepper, and pimentón and let simmer, uncovered, until the squash is tender but not soft, about 20 minutes. Meanwhile, chop the parsley. After squash is done, add half the parsley and mix well. Adjust seasoning, if needed.
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To serve, ladle into bowls and top with more parsley and plenty of freshly grated parmesan cheese.