Preheat oven to 450 °F. Place vegetables in the bottom of a large roasting pan. Season with salt and pepper, and half the chopped rosemary. Scatter lemon slices and half the cubed butter.
Season chicken generously with salt and pepper, stuff cavity with rosemary sprigs and quartered lemon. Place chicken, breast-side down, in a V-shaped roasting rack nestled on top of vegetables. Sprinkle the remaining chopped rosemary and the remaining cubed butter on top of chicken.
Roast the chicken for at least 75 minutes total, as follows: After the first 25 minutes (breast-side down), turn the chicken on its side and roast it for 25 more minutes, then turn chicken on its other side and roast it for an additional 25 minutes. If the chicken is not done (internal temperature of 165-degrees), roast it breast-side-down until it reaches the proper temperature. The breast of the chicken should never be up during roasting, hence 'upside down' chicken.
Remove the chicken and vegetables from the oven, and let them rest for at least 15 minutes before arranging them on a warm serving platter. Garnish the chicken and vegetables with rosemary sprigs, and serve.
