Step 1Heat onions in 3 1/2- to 4-quart saucepan or Dutch oven over medium heat. Add garlic and saute until softened, about 2 minutes. Sprinkle flour over top and cook, stirring continuously, until flour is absorbed and cooked through, about 2 minutes. Add beef and chicken broth, thyme, salt, sugar, and pepper to taste. Simmer 15 minutes. Remove from heat and stir in creme fra^iche.
Step 2Place 1 piece toasted bread in each soup bowl. Ladle soup over top. Garnish with grated Parmesan and serve immediately.