Combine chuck, parsley, scallion, salt, and pepper. Divide evenly into 4 portions and shape into 3/4 to 1-inch thick oval patties.
Place 2 tablespoons of flour in a shallow dish; dredge each patty in flour. Reserve 1 teaspoon flour.
Heat 1 tablespoon oil in a sauté pan over medium-high heat. Add patties and sauté 3 minutes on each side, or until browned. Remove from pan.
Add onions and sugar to pan; sauté 5 minutes. Stir in garlic and tomato paste; sauté 1 minute, or until paste begins to brown. Sprinkle onions with reserved flour; cook 1 minute. Stir in broth and wine, and then add the salt and thyme.
Return meat to pan and bring soup to a boil. Reduce heat to medium-low, cover and simmer 10 minutes.
Serve steaks on Cheese Toasts with onion soup ladled over.