In a large pot, heat olive oil over medium heat. Add the chopped onion, bell pepper, and celery. Sauté for 5-7 minutes until softened.
Stir in the minced garlic and sauté for another minute until fragrant.
Add the diced potatoes, vegetable broth, Cajun seasoning, and smoked paprika. Bring to a boil, then reduce heat and let simmer for about 20 minutes or until the potatoes are tender.
Once the potatoes are cooked, use an immersion blender to blend the soup to your desired level of creaminess (you can also blend in batches in a blender if you prefer).
Stir in the heavy cream and season with salt and pepper to taste. Heat through for another 5 minutes, allowing the flavors to meld together.
Serve hot, garnished with chopped green onions and fresh parsley.