Prepare the Vegetables: Wash and peel the potatoes, chop them into bite-sized chunks. Dice the onion, mince the garlic, slice the carrots, and chop the celery.

Sauté Onions and Garlic: In a large pot over medium heat, add olive oil and warm it. Once hot, add the diced onions and minced garlic, sauté for 3-5 minutes until translucent.

Add Carrots and Celery: Incorporate sliced carrots and chopped celery, stirring to combine, and sauté for an additional 5 minutes until softened.

Stir in Potatoes and Spices: Add the chopped potatoes and Cajun spice mix to the pot, stir well to coat the vegetables and cook for a minute.

Pour in the Broth: Carefully pour in vegetable broth, ensuring the contents are submerged. Bring to a boil then reduce heat and simmer for about 20 minutes until fork-tender.

Blend Until Smooth: Use an immersion blender to blend the soup until smooth, or transfer batches to a regular blender.

Stir in Heavy Cream: Return to medium heat, stir in heavy cream, and heat through for 3-5 minutes.

Season to Taste: Finally, season with salt and pepper to taste, adjusting Cajun spice as necessary.