In a large pot over medium-high heat, melt the butter and olive oil.
Add mushrooms and onions. Cook for about 10 minutes, stirring occasionally, until tender and browned.
Add garlic and sauté for 1-2 minutes.
Sprinkle in flour and stir continuously for 2 minutes to cook out the raw flavor.
Gradually add the chicken broth while stirring to avoid lumps.
Bring to a boil, then reduce to a simmer for 10 minutes.
Stir in heavy cream, salt, pepper, and thyme.
Simmer for another 5 minutes. Taste and adjust seasoning as needed.
Serve hot, garnished with fresh parsley if desired.