1. Sauté the vegetables:
In a large pot, heat the butter and olive oil over medium heat. Add the onion and garlic, and sauté until the onion becomes soft and translucent(about 5 minutes).

2. Cook the mushrooms:
Add the sliced mushrooms to the pot and cook for 8–10 minutes, stirring occasionally, until the mushrooms release their moisture and begin to brown.

3. Make the soup base:
Sprinkle the flour over the mushrooms (if using) and stir for 1–2minutes to cook off the raw taste. Then, gradually pour in the broth while stirring, making sure to scrape any browned bits from the bottom of the pot.Bring to a simmer.

4. Add the cream and season:
Once the broth is simmering, stir in the heavy cream (or milk). Add the thyme, and season with salt and pepper to taste. Let the soup simmer for another 5–10 minutes until thickened slightly.

5. Blend (optional):
For a smooth soup, use an immersion blender directly in the pot to blend the soup until creamy. Alternatively, you can transfer the soup in batches to a blender and puree until smooth.

6. Serve:
Ladle the soup into bowls and garnish with fresh parsley if desired.Serve hot with crusty bread or a side salad.

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