Heat olive oil in a large stockpot or Dutch oven over medium-high heat.
Add the onion, celery, and carrots. Saute until soft, about 8–10 minutes.
Add the garlic, rosemary, thyme, bay leaf, salt, and pepper saute for another minute.
Add the mushrooms and cook until they start to turn brown and have released a lot of their liquids, about 12–15 minutes.
Sprinkle the flour over the mushrooms, stirring continuously cook for 2–3 minutes.
Add the white wine, stir and cook for a few minutes, until it's bubbly and thick.
Add the wild rice and vegetable broth, bring back to a boil.
Simmer for 45 minutes or until wild rice starts to burst.
Stir in the heavy cream, cover and cook gently for another 5 minutes.
Season to taste with more salt and pepper.