In a large pot, heat olive oil over medium heat. Add chopped onion, celery, and carrot. Sauté until softened, about 5 minutes.

Add minced garlic and sauté for an additional minute until fragrant.

Add diced potatoes and chicken broth to the pot. Bring to a boil, then reduce heat and simmer for 20 minutes or until potatoes are tender.

Using an immersion blender, blend the soup until smooth. Alternatively, carefully transfer to a blender in batches.

Stir in heavy cream, Cajun seasoning, salt, and black pepper. Heat through for another 5 minutes.

Ladle the soup into bowls and garnish with chopped green onions.