Brown the sausage: Heat a large, deep skillet or Dutch oven over medium-high heat. Add the oil or butter, then the sliced smoked sausage. Cook until browned on both sides, about 4–6 minutes.
Transfer to a plate and leave the flavorful drippings in the pan.
Soften the aromatics: Reduce heat to medium. Add the onion with a pinch of salt and cook until translucent, 3–4 minutes. Stir in the garlic and cook 30 seconds, just until fragrant.
Don’t let it brown.
Build the base: Stir in the Italian seasoning, smoked paprika, and crushed red pepper if using. Add the broth and crushed tomatoes. Scrape up any browned bits from the bottom of the pan—those carry tons of flavor.
Add pasta and simmer: Stir in the dry pasta and bring to a gentle boil.
Lower heat to a steady simmer, cover, and cook 8–10 minutes, stirring once or twice to prevent sticking. Cook until the pasta is al dente. If the liquid gets too low before the pasta is done, add a splash of broth or water.
Return the sausage: Stir the browned sausage back into the pan.
Let everything bubble together for 1–2 minutes to mingle the flavors.
Make it creamy: Reduce the heat to low. Stir in the heavy cream. Simmer gently for 2–3 minutes to slightly thicken.
Avoid a hard boil here to keep the sauce smooth.
Add the cheese: Remove the pan from the heat. Sprinkle in the cheddar, mozzarella, and Parmesan a handful at a time, stirring between additions until melted and velvety. Season with salt and black pepper.
If the sauce feels too thick, loosen with a splash of warm broth or cream.
Finish and serve: Let the pasta rest for 2 minutes so the sauce sets and clings. Top with chopped parsley. Serve hot, with extra Parmesan at the table.