Dice the carrots, celery, and onion into uniform pieces.
Peel and chop the potatoes into cubes.
Cook the bacon until crispy. Set aside, and chop when cool. If using the same pot for soup, leave the bacon grease in the pot. If baking bacon in the oven, use olive oil for sautéing vegetables.
Add the diced carrots, celery, and onion to the pot with bacon grease (or olive oil). Sauté over medium-high heat for about 3 minutes.
Add the chopped potatoes, Creole seasoning, salt, and pepper. Cook for about 5 minutes, stirring occasionally.
While the vegetables cook, grate the Colby Jack cheese and mince the parsley. In a small bowl, whisk together the milk and flour to make a slurry.
Add the chicken broth to the pot. Bring to a gentle boil and cook until potatoes are tender, about 10–12 minutes.
Stir in the milk-flour slurry. Allow the soup to thicken, cooking for an additional 5 minutes.
Working in batches, carefully blend the soup in a blender or food processor until smooth. Transfer the pureed soup to a 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.