In a large pot, heat the olive oil over medium heat. Add the diced onion, garlic, bell pepper, carrots, and celery. Sauté for about 5-7 minutes, or until the vegetables are softened.
Add the chicken broth and cubed potatoes to the pot. Stir in the Cajun seasoning, smoked paprika, salt, and black pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for about 20 minutes, or until the potatoes are tender.
Once the potatoes are cooked, use a potato masher to mash some of the potatoes in the pot for a creamier texture, leaving some chunks for heartiness.
Stir in the heavy cream and let the soup simmer for an additional 5 minutes. Adjust seasoning to taste.
Serve hot, garnished with chopped green onions and parsley.