In a large pot, heat the olive oil over medium heat. Add the sliced smoked sausage and cook until browned. Remove the sausage and set aside.
In the same pot, add the chopped onion, garlic, bell pepper, and celery. Sauté until the vegetables are softened, about 5 minutes.
Add the chicken broth, diced potatoes, diced tomatoes (with juice), Cajun seasoning, thyme, and oregano. Stir to combine.
Bring the mixture to a boil, then reduce the heat to a simmer. Cover and cook for about 15-20 minutes, or until the potatoes are tender.
Return the sausage to the pot and stir in the heavy cream, if using. Heat until warmed through.
Taste and adjust seasoning with salt, pepper, and more Cajun seasoning if desired.
Serve hot, garnished with chopped green onions and/or parsley.
