In a large pot over medium heat, add the oil. Once hot, add the sausage and cook, stirring occasionally, until browned, about 3-4 minutes. Remove the sausage and set it aside.
In the same pot, add the onion, celery, and bell pepper. Cook until softened, about 5-8 minutes. Add garlic and cook for 1 additional minute.
Add the Cajun seasoning, salt, black pepper, paprika, cayenne pepper, chicken broth, and potatoes to the pot. Reduce heat and let the soup simmer for 20-25 minutes, or until the potatoes are tender.
Return the sausage to the pot, adding in the heavy cream and shredded cheese. Simmer for an additional 5 minutes or until everything is heated through and the cheese is melted.
Garnish with chopped parsley and serve warm.
