Heat the olive oil in a large pot over medium heat.
Add diced onions, celery, bell pepper, and garlic to the pot. Sauté until softened.
Stir in the diced potatoes and Cajun seasoning, ensuring the potatoes are evenly coated.
Pour in the broth and bring to a boil. Reduce heat and simmer for 20-25 minutes.
Once the potatoes are fork-tender, use a potato masher to partially mash the soup.
Stir in the heavy cream and season with salt and pepper to taste.
Serve hot, garnished with green onions or parsley if desired.