In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.

Add the minced garlic, diced carrots, and diced celery. Cook for another 5 minutes until the vegetables are softened.

Stir in the sliced mushrooms and cook until they release their moisture and become tender, about 5-7 minutes.

Add the rinsed wild rice, vegetable broth, thyme, salt, and black pepper. Bring to a boil, then reduce heat to low and simmer for 30-35 minutes, or until the rice is tender.

If using, stir in the heavy cream just before serving. Adjust seasoning if necessary.