Place a large pot or Dutch oven over medium heat and add the vegetable oil. Once shimmering, add the sliced andouille sausage. Cook, stirring occasionally, until the sausage is well-browned and has rendered some of its flavorful fat, about 4-5 minutes. The sausage is key to the soup's flavor, much like in our popular Cajun Sausage and Rice Skillet. Use a slotted spoon to transfer the sausage to a separate plate, leaving the rendered fat in the pot.

To the same pot, add the diced onion, celery, and red bell pepper. Sauté over medium heat, stirring occasionally, until the vegetables have softened, about 6-8 minutes. Add the minced garlic and cook for another minute until fragrant, being careful not to let it burn.

Sprinkle the Cajun seasoning, salt, pepper, paprika, and cayenne pepper over the vegetables and stir to combine. Cook for 30 seconds to toast the spices. Pour in the chicken broth, add the cubed potatoes, and stir in 1 teaspoon of Worcestershire Sauce. Stir everything together, scraping up any browned bits from the bottom of the pot.

Bring the soup to a gentle boil, then reduce the heat to low, cover, and let it simmer for 20-25 minutes, or until the potatoes are completely tender and can be easily pierced with a fork.

Once the potatoes are tender, you can use an immersion blender to pulse the soup a few times directly in the pot. This will thicken the soup naturally without flour. For a smoother soup, blend more; for a chunkier soup, blend less.

Return the cooked andouille sausage to the pot. Stir in the heavy cream and shredded cheddar cheese. Continue to simmer gently over low heat for another 5 minutes, stirring until the cheese is fully melted and the soup is heated through. Do not let it boil after adding the cream. Taste and adjust seasonings if necessary. Garnish with fresh parsley and serve hot.