In a small bowl, combine cornstarch with 1 cup of the beef broth. Whisk and let sit.
In a large sauce or stock pan, melt butter over medium heat. Add the onions and mushrooms and cook until the mushrooms have released their moisture and it has evaporated, about 12-15 minutes.
Add the garlic and thyme and cook until fragrant, about 1 minute.
Add the wine and cook until it is absorbed.
Add the cornstarch mixture and remaining 3 cups of beef broth and the beef. Bring to a boil, reduce the heat and simmer for 15 minutes.
Mix in the parsley and remove from heat. Let sit 5 minutes and soup will continue to thicken.
Give a final stir and serve. Squeeze lemon wedges over finished soup also, if desired.