Tie the duck legs together with kitchen twine and fold the wing tips under the body. Season all over with salt and pepper. In a large Dutch oven with a tight-fitting lid, heat the oil until shimmering. Sear duck on all sides over moderately-high heat until golden brown, about 8 minutes. Transfer the duck to a plate.
Add carrots, celery, onion and peppercorns and cook over moderate heat, stirring, until lightly browned, about 8 minutes. Add the white wine, chicken stock, bay leaves, thyme and 1 tablespoon of salt. Bring to a simmer, then return the duck to pot. Cover and simmer until the duck is very tender and the meat is falling off the bone, about 1½ hours.
Transfer the duck to a plate and let cool slightly. Discard the thyme sprigs and bay leaves. Remove the skin and fat and return the skin and fat to the pot. Pick off all the meat and reserve, keeping warm. Discard the bones. Puree the cooking liquid and skin in a blender (the skin and the fat thicken and emulsify the sauce) and strain through a fine mesh sieve set over a clean pot. Season to taste. Fold the shredded meat into the sauce.
Add the butter and tomatoes to the ragout and simmer over medium heat until you reach a thick sauce-like consistency, about 3 to 5 minutes.
Meanwhile, cook the pasta according to package directions. Toss the freshly cooked pasta with the finished ragout. Transfer to shallow bowls and garnish with chives; serve.