Add the chopped onion, bell pepper, and celery to the same pot. Cook for 2 to 3 minutes until softened. Then, add the minced garlic and cook for another minute.

Stir in the butter and flour. Mix well to form a paste and cook for 2 to 3 minutes to eliminate the raw flour taste.

Gradually add the chicken broth and half and half to the pot, stirring constantly to combine. Add the cubed potatoes and Cajun seasoning. Lower the heat to medium-low and simmer for 20 to 25 minutes, or until the potatoes are fork-tender, stirring occasionally.

Once the potatoes are tender, add the cooked sausage and shredded cheddar cheese to the soup. Stir until the cheese is melted and everything is well combined.

Remove from heat and let the soup cool slightly before ladling into bowls. Garnish with fresh parsley before serving.