Preheat oven to 425 degrees F.
Wash the chicken in hot water and dry thoroughly. Season the cavity with salt and black pepper and stuff with the onion, lemon, and celery leaves. Rub the chicken lightly with softened butter and season all over with salt and pepper. Tie the drumsticks ends together and set the chicken, breast side up, in an oiled v-shaped rack or on an oiled roasting pan in the oven.
Roast for 15 minutes at 425 degrees F, then reduce the heat to 350 degrees, baste the chicken, and roast for 15 minutes. Add the chopped onion and carrot to the pan, basting them and the chicken. Continue roasting the chicken until the juices run clear, for a total of 45 minutes plus an additional 7 minutes for each pound. (In other words, a 3 1/2 pound chicken would take a basic 45 minutes plus an additional 25 minutes, for a total 70 minutes or 1 hour and 10 minutes of cooking time.)
Remove the chicken and spoon the fat out of the roasting pan. Into the pan, stir in the herbs and blend in the broth and, stirring constantly, boil for several minutes on the stovetop to concentrate the flavor. Correct the seasoning and strain the sauce into a warm sauceboat. Carve the chicken and serve with the warm sauce.
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