To a large pot and over medium heat, add the oil. Once hot, add the sausage and cook, stirring occasionally until browned, about 3-4 minutes. Remove the sausage from the pan and set aside on a plate or in a bowl while you prepare the rest of the soup.

To the same pot over medium heat, add the onion, celery, and bell pepper. Cook until softened, about 5-8 minutes. Add garlic and cook for 1 more minute.

To the pot, add Cajun seasoning, salt, pepper, paprika, cayenne pepper, chicken broth, and potatoes. Reduce heat. Simmer for 20-25 minutes, or until the potatoes are fork-tender.

Return the sausage to the pot and add in heavy cream and shredded cheese. Let the soup simmer for an additional 5 minutes, or until everything is heated through and the cheese is melted.

Garnish with parsley. Serve warm.