2. Using both hands, tension a piece of kitchen twine, slide it under the front of the cavity, and tie a loose knot around the ends of the drumsticks.
3. Place the chicken backside down in a deep pan that holds it comfortably with several inches of space all around. Add the vegetables and herbs and only enough water to reach the top of the drumstick, leaving most of the breast exposed.
4. Lightly salt the water, bring to a boil, skim away the froth that rises to the surface, then reduce it immediately to a bare simmer.
5. Cook the chicken for 30 to 35 minutes. Test the thigh and legs for tenderness with the tip of a knife. Carefully invert the chicken breast side down. Simmer the chicken for an additional 15 minutes, then turn the chicken backside down again, turn off the heat, and cover the pot.
6. Combine the bread crumbs with the melted butter in a pie pan and toast them to golden brown in a moderate oven. Add the chicken cooking liquid to the toasted bread.
7. Pass the bread and broth through the finest sieve of the food mill. If the sauce is coarse, pass it again until you achieve a smooth consistency.
8. Stir in the pepper, salt, and balsamico. Keep warm over warm water.
9. Cut the chicken into serving pieces and remove its skin. Divide the chicken among 4 plates and nap each piece with the vinegar sauce. Serve with buttered peas or carrots.
Adam Rapoport, editor in chief of Bon Appetit magazine and the website www.bonappetit.com, knows his way around a grill. He has edited an entire book on the subject: The Grilling Book: The Definitive Guide from Bon Appetit.