Heat butter and oil in a large Dutch oven over medium-high heat until melted. Sauté onion for 2 to 3 minutes until softened; add garlic and cook until fragrant, about 1 minute.
Add sliced mushrooms and two teaspoons of fresh thyme, and cook for 5 minutes.
Sprinkle mushrooms with flour, mix well and cook for 2 minutes. Add the chicken broth, mix again and bring to a simmer. Reduce heat to low-medium heat, and season with salt and pepper.
Cover the mushroom soup and allow to simmer for 10-15 minutes, while occasionally stirring, until the soup has thickened.
Reduce heat to low, and stir in cream. Allow to gently simmer (do not boil). Adjust seasoning if you like. Mix in parsley and remaining thyme. Serve the creamy mushroom soup immediately.
