Bring a large pot of generously salted water to a rolling boil. Cook campanelle according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

While the pasta cooks, heat olive oil in a large skillet over medium-high heat. Add sausage, breaking it into crumbles with a wooden spoon. Cook until deeply browned and cooked through (internal temperature 160°F/71°C), about 6–8 minutes.

Reduce heat to medium. Add garlic and red pepper flakes, stirring for 30 seconds until fragrant. Add kale in handfuls, tossing with tongs until wilted, about 3–4 minutes.

Pour in white wine (or broth) and scrape up any browned bits from the pan. Let it simmer until reduced by half, about 2 minutes. Stir in heavy cream and bring to a gentle simmer.

Add the drained campanelle to the skillet along with the Parmesan cheese. Toss everything together, adding reserved pasta water a little at a time until the sauce is silky and clings to the pasta.

Taste and adjust seasoning with salt and pepper. Transfer to a serving bowl, top with additional Parmesan and red pepper flakes. Serve immediately.