Heat olive oil in a soup pot over medium heat. Remove the sausage from its casing, break it apart, and cook until golden brown, about 5-7 minutes. Reserve the cooked sausage on a plate.

In the same pot, add diced onion, celery, and carrots to the rendered fat. Sauté for 10 minutes until softened, then stir in minced garlic and dried thyme for an additional minute until fragrant.

Sprinkle all-purpose flour into the vegetable mixture, stirring well until a paste forms. Cook for another 2-3 minutes until the flour is lightly golden.

Gradually pour in chicken or vegetable stock, deglazing the pot while stirring. Add bay leaves and wild rice, bringing the mixture to a simmer for about 30 minutes.

Incorporate the cubed russet potatoes into the pot, cooking for an additional 15 minutes or until the potatoes are tender.

Stir in the cream, mixing until combined. Season with salt and pepper to taste, serving hot.