Dice the carrots, celery, and onion into uniform pieces.

Peel and chop the potatoes into 1/2-inch cubes.

Cook the bacon in a large pot or Dutch oven over medium heat until crispy; set aside on a paper towel-lined plate to cool, then chop. Leave the bacon grease in the pot. If not using bacon, add 1 tablespoon of olive oil to the pot.

Add the diced carrots, celery, and onion to the pot with the bacon grease (or olive oil). Sauté over medium-high heat for about 3 minutes until softened.

Stir in the chopped potatoes, Creole seasoning, salt, and black pepper. Cook for about 5 minutes, stirring occasionally, to let the potatoes absorb the flavors.

While vegetables cook, grate the Colby Jack cheese and mince the parsley. In a small bowl, whisk together the milk and flour until smooth to create a slurry.

Pour the chicken broth into the pot. Bring to a gentle boil, then reduce heat and simmer until the potatoes are tender, about 10-12 minutes.

Stir in the milk-flour slurry. Allow the soup to thicken, cooking for an additional 5 minutes, stirring frequently to prevent sticking.

Carefully transfer the soup in batches to a blender or use an immersion blender directly in the pot. Blend until the soup is smooth and creamy. If using a regular blender, fill only halfway and vent the lid to release steam.

Return all the pureed soup to the clean pot. Slowly heat the pureed soup over low heat. Stir in the heavy cream and minced parsley. Taste and adjust seasoning if needed.

Ladle the soup into bowls. Top each serving with grated cheese, chopped bacon, and extra parsley if desired. Serve hot.