Melt the butter in a large saucepan over medium-high heat. Add the mushrooms and cook, stirring occasionally, until dry and tender, about 10 minutes. Season with salt and pepper.
Sprinkle the flour over the mushrooms and cook, stirring until lightly browned, about 1 minute. Add the Marsala and broth and continue to cook until it comes to a boil and thickens, about 5 minutes. Stir in the thyme and adjust the seasoning with salt and pepper.
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