Combine chuck, parsley, scallion, salt and pepper. Divide evenly into 4 portions and shape each into 3/4"-1" thick oval patties. Place 2 tablespoons flour in a shallow dish; dredge each patty in flour. Reserve 1 teaspoon flour.
Heat 1 tablespoon oil in a saute pan over medium-high heat. Add patties and saute 3 minutes on each side, or until browned. Remove from pan.
Add onions and sugar to pan; saute 5 minutes. Stir in garlic and tomato paste; saute 1 minute, or until paste begins to brown. Sprinkle onions with reserved flour; cook 1 minute. Stir in broth and wine, then add the salt and thyme.
Return meat to pan and bring soup to a boil. Reduce heat to medium-low, cover and simmer 20 minutes.
Serve steaks on Cheese Toasts with onion soup ladled over. Garnish with parsley and Parmesan.