1. Preheat oven to 450°.
2. To prepare stock, arrange first 5 ingredients in a single layer on a large baking sheet. Bake at 450° for 35 minutes or until browned. Scrape beef mixture and pan drippings into a large Dutch oven. Stir in 3 quarts cold water and next 4 ingredients (through bay leaf); bring to a boil over medium heat. Reduce heat to low, and simmer 2 1/2 hours, skimming surface as necessary. Strain mixture through a fine-mesh sieve lined with a double layer of cheesecloth over a bowl; discard solids. Wipe pan clean with paper towels.
3. To prepare soup, return Dutch oven to medium heat. Add oil to pan; swirl to coat. Melt butter in oil. Add sliced onion to pan; cook for 5 minutes, stirring occasionally. Partially cover, reduce heat to medium-low, and cook 15 minutes, stirring occasionally. Add salt and ground pepper; cook, uncovered, until deep golden brown (about 35 minutes), stirring frequently. Add reserved stock and chopped thyme; bring to a boil. Reduce heat, and simmer until reduced to 8 cups (about 50 minutes). Stir in chives.
4. Preheat broiler to high.
5. Arrange bread slices in a single layer on a jelly-roll pan, and broil for 2 minutes or until toasted, turning after 1 minute. Ladle 1 1/3 cups soup into each of 6 broiler-safe soup bowls. Top each serving with 2 bread slices, and sprinkle evenly with cheese. Place soup bowls on jelly-roll pan, and broil for 4 minutes or until tops are golden brown and cheese bubbles.