Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the sliced sausage and cook until lightly browned, about 3 to 4 minutes. Remove the sausage with a slotted spoon and set aside, leaving any rendered fat in the pot.
Add the chopped onion and bell pepper to the pot. Cook until softened, about 5 minutes.
Stir in the minced garlic, Cajun seasoning, thyme, and black pepper. Cook for 1 minute until fragrant.
Pour in the diced tomatoes (with their juice) and the chicken broth. Bring the mixture to a boil.
Add the dry pasta to the boiling liquid. Stir well to prevent sticking. Reduce the heat to medium-low, cover the pot, and simmer for 10 to 12 minutes, or until the pasta is cooked al dente, stirring occasionally.
Stir in the cooked sausage, heavy cream, and Parmesan cheese. Cook uncovered for 2 to 3 minutes until the sauce thickens slightly and everything is heated through. Do not boil after adding the cream.
Taste and add more Cajun seasoning if you want more heat. Garnish with fresh parsley before serving.
Notes
If the sauce seems too thick, add a splash more broth or milk until you reach your desired consistency.
Use low-sodium broth if you are watching your salt intake, as sausage and Cajun seasoning already contain salt.
For extra richness, substitute half-and-half for the heavy cream.