Heat butter in a large pot, over medium heat. Sauté onions, mushrooms, and thyme, until softened, about 5 minutes.
Sprinkle mushrooms with flour, mix well, and cook for 2-3 minutes.
Add stock, and bring to a boil. Reduce to a medium low, and allow soup to simmer for 15-20 minutes, occasionally stirring, until thickened.
Reduce heat to low, stir in cream or half and half. Allow to gently simmer (do not boil, or dairy will curdle). Season with salt and pepper to taste. Start with lower amount of salt and pepper, adjust as needed. Serve warm.
