Melt the butter in a large heavy-bottomed pot or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 5 minutes.

Add the sliced mushrooms and dried thyme to the pot. Sauté, stirring occasionally, until the mushrooms have released their liquid and started to brown, about 10-12 minutes. This step is key for deep flavor.

Stir in the minced garlic and cook for 1 minute until fragrant. Sprinkle the flour over the mushroom mixture and stir constantly for 1 minute to cook out the raw flour taste (making a roux).

Gradually whisk in the chicken broth, ensuring no lumps form. Bring the mixture to a simmer, scraping up any browned bits from the bottom of the pot. Reduce heat and cook for 10 minutes to allow the flavors to meld and the soup to thicken slightly.

Remove the soup from the heat. Use an immersion blender to blend the soup until it reaches your desired consistency (about half blended for a chunky texture, or fully blended for creamy smoothness). Alternatively, carefully transfer half the soup to a standard blender and blend until smooth before returning it to the pot.

Stir in the heavy cream. Season generously with salt and freshly ground black pepper to taste. Heat gently for 2-3 minutes until warmed through (do not boil after adding cream).

Ladle the creamy mushroom soup into bowls. Garnish with fresh chopped parsley and serve immediately, perhaps with crusty bread.