Melt the butter in a large pot over medium-high heat. Add the mushrooms and cook, stirring occasionally, until browned and tender, about 7 minutes.

Reduce heat to medium. Add the onion and cook until soft, about 3 minutes. Stir in the garlic and turmeric, cook 1 minute more.

Sprinkle in the flour and stir for 1 minute. Gradually whisk in the vegetable broth, scraping up any browned bits, and bring to a boil.

Reduce heat to low and simmer uncovered for 10 minutes, stirring occasionally, until slightly thickened.

Remove from heat. Stir in the heavy cream, season with salt and pepper. Blend briefly with an immersion blender if desired. Ladle into bowls and garnish with fresh thyme.