Estimated roasting time for a 5 lb chicken is 2 hours.
Preheat oven to 425°. Sprinkle the chicken (inside and out) with salt. Rub skin of chicken with 2 TBS butter. In a small bowl, combine 2 TBS butter with the olive oil.
Place the chicken, breast up, on an adjustable wire rack inside a large shallow roasting pan. Strew the vegetables directly into the roasting pan and place the pan in the middle of the preheated oven. Allow the chicken to brown lightly for 15 minutes, turning it on the left side after 5 minutes, on the right side for the last five minutes, basting with the combined butter and oil after each turn. Reduce the heat to 350°. Leave the chicken on its side and baste every 10 minutes, using the fat in the roasting pan once all of the butter and oil have been used. Carefully watch the temperature and regulate the heat so the chicken is making "cooking noises", but the fat is not burning.
Halfway through the estimated cooking time, turn the chicken on its other side and continue basting every 10 minutes. Fifteen minutes before the end of the estimated roasting time, turn the chicken breast up and continue basting. Indications that the chicken is almost done are a sudden rain of splutters, a swelling of the breast, the drumstick is tender when pressed and can be moved in its socket. Another check is to prick the thickest part of the drumstick with a fork. The juices should run clear yellow. When done, set the chicken on a hot platter for at least ten minutes prior to carving.
Remove all but 4 TBS of fat from the pan (leaving the slightly charred vegetables in the pan as an addition to the sauce). Add the chicken broth and boil rapidly over high heat, constantly stirring. Reduce liquid to about one cup and remove from heat. Add the butter and season to taste. Place sauce in serving dish. Carve the chicken and put onto a serving platter. Pass the sauce separately at the table. 4 servings.