Preheat the oven to 425°F. Melt 1 tablespoon of the butter in a skillet. Add the diced carrots, onion, and celery and cook over moderate heat until softened. Stir in the herbs and set aside.

If desired, cut out and discard the wishbone. Pull the neck skin up over the chicken breast and secure it to the back with a toothpick.

Salt and pepper the cavity and spoon in the cooked vegetables, a handful of parsley stems and celery leaves, and the lemon slices. Massage the chicken all over with 1 tablespoon of the butter, then truss it. Alternatively, tie drumstick ends together and tuck wings under the body.

Choose a flameproof roasting pan that is about 1 inch larger than the chicken and place a rack inside. Salt the chicken all over and set it breast-side up on the rack.

Roast the chicken for 15 minutes and then brush with the remaining ½ tablespoon butter. Scatter the sliced onion and carrot all around. Reduce the oven temperature to 350°F.

Roast for 45 minutes, and then brush the lemon juice over the chicken. If necessary, add ½ cup of water to the vegetables to prevent burning.

Roast for 1 hour and baste the chicken with pan juices. Test for doneness; drumsticks should move easily in their sockets and their flesh should feel somewhat soft. If not, continue roasting, basting and testing every 7 to 8 minutes, until an instant-read thermometer registers 165°F.

Spear the chicken through the shoulders and lift to drain; if juices run clear yellow, the chicken is done. Let the chicken rest on a carving board for 15 minutes; discard the string.

Spoon all but 1 tablespoon of fat from the juices in the pan. Add the stock and boil until lightly syrupy, 5 minutes. Strain; you will have just enough to bathe each serving with a fragrant spoonful.