Heat the butter and olive oil in a large pot or Dutch oven over medium heat. Add the chopped onions and sauté until soft and translucent, about 5 minutes.
Add the sliced mushrooms to the pot. Cook until they have released their moisture and become deeply browned, about 8 to 10 minutes. Stir in the minced garlic and thyme, cooking for 1 more minute until fragrant.
Sprinkle the flour over the mushroom mixture and stir well to coat. Cook for 1 to 2 minutes to remove the raw flour taste.
Pour in the white wine to deglaze the pan, scraping up any browned bits from the bottom. Allow the wine to reduce by half.
Gradually whisk in the vegetable broth, ensuring there are no flour lumps. Bring the soup to a gentle simmer and let it cook for 15 minutes to allow the flavors to meld and the soup to thicken.
Reduce the heat to low and stir in the heavy cream, salt, and black pepper. Let the soup warm through for 2 to 3 minutes without bringing it to a boil to prevent curdling.
Serve hot, garnished with extra fresh thyme or a drizzle of olive oil, if desired.