In a large pot, heat the olive oil over medium heat. Add the chopped onion, bell pepper, and celery, sautéing until softened, about 5 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the diced potatoes to the pot, along with the Cajun seasoning, smoked paprika, black pepper, and cayenne. Stir to coat the vegetables evenly with the spices.
Pour in the vegetable broth and bring the mixture to a boil. Reduce heat and let it simmer for about 20-25 minutes, or until the potatoes are tender.
Once the potatoes are cooked, use a potato masher or an immersion blender to blend the soup to your desired consistency. For a creamier texture, blend thoroughly; for a chunkier soup, blend partially.
Stir in the heavy cream (or coconut milk) and bring the soup back up to a gentle simmer. Taste and adjust seasoning with salt if needed.
Serve hot, garnished with chopped green onions and fresh parsley for an extra pop of color and flavor.
Notes
For a dairy-free option, use coconut milk instead of heavy cream.