Prepare Your Ingredients: Wash and peel the potatoes, chop them into cubes, dice the onion, slice the carrots, and chop the celery. Gather your Cajun spices, broth, cream, and optional ingredients.

Sauté the Vegetables: In a large pot over medium heat, heat olive oil and sauté diced onions, carrots, and celery for about 5-7 minutes until softened.

Add Potatoes and Spices: Add cubed potatoes and Cajun spices to the pot, stirring for 1-2 minutes until well-distributed.

Pour in the Broth: Slowly add the broth, bring to a gentle boil, then reduce heat and simmer uncovered for about 20 minutes until potatoes are tender.

Blend for Creaminess: Using an immersion blender, partially blend the soup to achieve a creamy consistency while keeping some potato chunks.

Stir in the Cream: Finally, add the cream or half-and-half, let it simmer for an additional 5 minutes on low heat.