In a large pot, cook the sliced mushrooms, onions, and thyme with the broth until they are tender, about 15 mins
Transfer the cooked mushroom mixture to the blender or food processor and pulse until pureed but still a bit chunky
In the same pot, melt the butter whisk in the flour, and cook the mixture for about a minute
Whisk in half-and-half until the flour dissolves, and pour in the mushroom mixture. Season with salt and pepper. Stirring constantly, bring the soup to a boil, and cook until thickened
Add the Marsala wine and adjust seasoning if needed