Melt butter in a large (6-quart) soup pot over medium-high heat; add onions and shallots. Cook, stirring frequently, 30 to 35 minutes or until onions are softened and a deep golden brown.
Tie thyme in a bundle with kitchen string, and add to onion mixture. Stir in caraway seeds, chicken stock, and veal broth. Bring to a boil; reduce heat, and simmer, uncovered, 20 minutes. Remove thyme; stir in salt and pepper.
Ladle soup into oven-safe bowls. Top with French bread slices, and sprinkle with cheese. Place bowls on a baking sheet; broil 2 minutes or until cheese melts and bubbles. Sprinkle each serving evenly with green onions and chives.
Brasserie Beck, Washington, DC
