In a large pot over medium heat, add the vegetable 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.

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

Add Cajun seasoning, kosher salt, black pepper, paprika, cayenne pepper, chicken broth, and cubed potatoes to the pot. Reduce heat and simmer for 20-25 minutes, or until the potatoes are fork-tender.

Return the sausage to the pot and stir 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 and serve warm.