In a large pot, heat olive oil over medium heat until shimmering, about 1-2 minutes.

Remove the sausage from its casings, breaking it into bite-sized pieces. Add the sausage to the pot, cooking until browned, about 6-8 minutes.

In the same pot, add chopped onion, sliced celery, and carrots. Sauté for about 10 minutes until the vegetables are softened.

Stir in minced garlic and dried thyme, cooking for another 30 seconds until aromatic.

Sprinkle all-purpose flour over the sautéed vegetables, stirring well to coat. Cook for about 2 minutes to form a roux.

Gradually whisk in broth, stirring constantly. Bring to a gentle simmer, about 3-5 minutes.

Once simmering, add bay leaves and wild rice. Reduce heat to medium-low, cover, and let simmer for about 30 minutes.

After 30 minutes, add chunked potatoes. Let simmer uncovered for an additional 15 minutes until fork-tender.

Gently stir in light cream or half and half to warm the mixture without boiling, about 2-3 minutes.

Remove bay leaves, taste, and adjust seasoning with salt as needed. Serve hot, garnished with fresh parsley if desired.