In a large Dutch oven or heavy-bottomed pot, melt the butter with olive oil over medium heat.

Add the chopped onion and sauté for 5-7 minutes until softened and translucent. Add the minced garlic and cook for 1 minute more until fragrant, being careful not to burn it.

Add the sliced mushrooms, dried thyme, and dried rosemary to the pot. Increase heat slightly to medium-high and cook the mushrooms, stirring occasionally, until they have released their liquid and started to brown deeply (about 10-12 minutes).

Sprinkle the flour over the mushroom mixture and stir constantly for 1 minute; this creates a roux to thicken the soup. Gradually whisk in the broth, ensuring there are no lumps. Bring the mixture to a simmer, scraping up any browned bits from the bottom of the pot.

Reduce the heat to low, cover, and let the soup simmer gently for 15 minutes to allow the flavors to meld.

Remove the pot from the heat. Use an immersion blender to blend about half of the soup until mostly smooth, leaving some chunks for texture, or blend all of it for a perfectly smooth consistency. Alternatively, carefully transfer half the soup to a standard blender and blend, then return it to the pot.

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

Ladle the hot soup into bowls, garnish with fresh parsley, and serve immediately.