In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Stir in the minced garlic, diced carrots, and diced celery. Cook for an additional 3-4 minutes until the vegetables begin to soften.
Add the cubed potatoes, chicken broth, Cajun seasoning, dried thyme, salt, and pepper. Bring to a boil, then reduce the heat and let it simmer for about 20-25 minutes, or until the potatoes are tender.
Once the potatoes are cooked, use a potato masher to mash some of the potatoes in the pot for a thicker texture, leaving some chunks for heartiness.
Stir in the heavy cream and let the soup heat through for another 5 minutes. Adjust seasoning if necessary.
If using, stir in the crumbled bacon just before serving.
Serve hot, garnished with sliced green onions and shredded cheddar cheese.