Heat the vegetable oil in a large pot over medium heat. Add the andouille sausage slices and cook them for 3 to 4 minutes, turning occasionally, until they develop a nice brown color. Remove the sausage and set aside temporarily.
In the same pot, toss in the diced onion, celery, and red bell pepper. Cook these vegetables on medium heat for about 5 to 8 minutes until they become tender. Add in the minced garlic and cook it for another minute, making sure it releases its aroma without burning.
Sprinkle in the Cajun seasoning, kosher salt, black pepper, paprika, and cayenne pepper. Pour in the chicken broth and add the cubed potatoes. Stir well to combine all ingredients, then bring the mixture to a gentle simmer. Lower the heat and let it cook for 20 to 25 minutes, or until the potatoes are soft when pierced with a fork.
Return the browned sausage to the pot once the potatoes are done. Mix in the heavy whipping cream and shredded cheddar cheese, stirring until the cheese melts completely. Let the soup simmer for an extra 5 minutes so everything is heated through and well blended.
Serve the soup hot, topped with freshly chopped parsley for a vibrant finish. Enjoy this comforting bowl of Cajun Potato Soup!
