Wash and chop the vegetables: dice the onion, bell pepper, carrots, and celery into small pieces. Mince the garlic cloves finely.
In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for 3-4 minutes until translucent. Stir in the minced garlic, bell pepper, carrots, and celery, and cook for an additional 5 minutes.
Add the peeled and diced potatoes along with the chicken broth. Sprinkle in the Cajun seasoning, smoked paprika, salt, and pepper. Bring to a boil, then reduce heat and let simmer for 20-25 minutes until the potatoes are tender.
Mash some of the potatoes in the pot to create a thicker texture, leaving some chunks for heartiness. Alternatively, use an immersion blender for a smoother soup.
Stir in the heavy cream and heat through for another 5 minutes. Adjust seasoning if necessary, then serve garnished with sliced green onions and chopped parsley.