In a large pot or Dutch oven, combine the potatoes, onion, celery, garlic, and chicken broth.
Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until the potatoes are tender.
Use an immersion blender to partially blend the soup, leaving some chunks for texture. Alternatively, carefully transfer half of the soup to a regular blender and blend until smooth, then return it to the pot.
Stir in the heavy cream and Cajun seasoning. Heat through, but do not boil.
Season with salt and pepper to taste. Serve hot, garnished with your favorite toppings.
Notes
Optional toppings include shredded cheese, bacon bits, sour cream, or chopped green onions.