1. Heat the butter or olive oil in a large pot over medium heat until melted and shimmering.
2. Add the chopped onions and sauté for about 5 minutes, stirring occasionally, until they become translucent and soft. This step builds the soup’s flavor base, so don’t rush it.
3. Stir in the minced garlic and cook for another 30 seconds, just until fragrant—be careful not to burn it.
4. Add the sliced mushrooms and thyme to the pot. Cook for about 8-10 minutes, stirring often, until the mushrooms release their moisture and start to brown. This caramelization adds depth to the soup.
5. Sprinkle the flour over the mushroom mixture and stir well to coat everything evenly. Cook for 1-2 minutes to eliminate the raw flour taste; you should see the mixture thicken slightly.
6. Slowly pour in the broth while stirring continuously to avoid lumps. Bring the soup to a gentle simmer and let it cook for 15 minutes, allowing the flavors to meld and the soup to thicken.
7. Remove the pot from heat and use an immersion blender to puree the soup until smooth and creamy. If you don’t have an immersion blender, carefully transfer the soup in batches to a blender and puree, then return it to the pot.
8. Stir in the milk or half-and-half, and return the pot to low heat. Warm the soup gently for 3-5 minutes—don’t boil, or the milk might curdle.
9. Taste and season with salt and pepper. If you want a richer flavor, stir in the Parmesan cheese at this point until melted.
10. Serve hot with your favorite crusty bread or a sprinkle of fresh herbs.

When I first tried making this soup, I skipped the caramelization step and ended up with a bland result. Trust me, taking the time to let the mushrooms brown is worth every minute—it’s where the magic happens.