Gather the ingredients.
Melt the butter in a large saucepan over medium-high heat.
When the butter starts to sizzle, add the mushrooms and cook, stirring for 10 minutes, or until the mushroom juices have evaporated and they begin to brown.
Stir in the flour, reduce the heat to medium, and cook for another 5 minutes.
Whisk in 1 cup of the cold broth.
Once incorporated, pour in the rest of the broth and add the thyme.
Bring back to a simmer, reduce the heat to low, and simmer gently for 30 minutes, stirring occasionally.
Season with salt and fresh ground black pepper to taste.