In a large pot, cook the sliced mushrooms, onions, and thyme in the broth until they are tender, about 15 mins
Transfer 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 the evaporated milk until flour is dissolved and pour in the mushroom mixture. Stirring constantly, bring the soup to a boil, and cook until thickened.
Add the Marsala wine and adjust seasoning if needed