1. Pat shortrib dry, then lightly season with salt and pepper. Heat oil in a large heavy pot over medium-high heat until it shimmers, then brownshortrib on all sides, 5 minutes total. Transfer to a plate.
2. Add onions, garlic, and 1 teaspoon salt to pot and cook, stirring occasionally, until onions are very soft and a browncrust forms on bottom of pot, about 30 minutes. Add Madeira, stirring and scraping up crust, then add stock, thyme, bay leaf, 1 teaspoon coarsely ground black pepper, 1/2 teaspoon salt, and shortrib with any juices from plate and simmer, covered, stirring occasionally, until shortrib is very tender, about 2 hours.
3. Discard bay leaf and thyme. Shred meat from shortrib with 2 forks (discard bone and gristle), then return to pot. Seasonsoup with salt and keep warm, covered, over low heat.
1. Preheat oven to 325 degrees Fahrenheit with rack in middle.
2. Halve baguette crosswise, then cut each half lengthwise into 3 (1/4-inch-thick) slices, transferring to a baking sheet. Brush both sides of bread with oil, then sprinkle with thyme and a pinch of salt. Bake until pale golden and dry, about 25 minutes.
3. Preheat broiler. Sprinkle toasts evenly with cheese and broil 3 to 4 inches from heat until cheese is melted and toast is golden in some spots, 1 to 2 minutes.
To serve: Ladle soup into bowls and sprinkle with chives. Serve with toasts.
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