Boil the pasta. Bring a large pot of salted water to a boil.
Cook the pasta until just shy of al dente. Reserve 1 cup of pasta water, then drain.
Brown the sausage. While the pasta cooks, heat olive oil in a large skillet over medium-high heat. Add the sausage and break it up with a spoon.
Cook until browned and cooked through, about 5–7 minutes. Spoon off excess fat if needed, leaving about a tablespoon for flavor.
Soften the aromatics. Add the chopped onion to the skillet and cook 2–3 minutes until translucent. Stir in the garlic and cook 30 seconds, just until fragrant.
Build the base. Stir in the tomato paste and crushed red pepper flakes.
Cook 1 minute to caramelize the paste—it should darken slightly. This step adds a deeper, richer taste.
Deglaze. Pour in the chicken broth and scrape up any browned bits from the pan. Simmer 1–2 minutes to reduce slightly.
Make it creamy. Reduce the heat to medium-low and stir in the heavy cream.
Add Italian seasoning. Simmer gently for 2–3 minutes until the sauce thickens slightly. Season with salt and pepper.
Add greens and cheese. Stir in spinach or kale until just wilted, 30–60 seconds.
Sprinkle in the Parmesan and stir until smooth and glossy.
Bring it together. Add the drained pasta to the skillet. Toss to coat, adding splashes of the reserved pasta water as needed to loosen the sauce and help it cling. The sauce should lightly coat the pasta without pooling.
Finish and serve. Taste and adjust seasoning.
Add a pinch of lemon zest if you like. Serve topped with extra Parmesan and chopped basil or parsley.