Preheat oven to 450˚F.
Using paper towels, pat dry the chicken.
Place the lemon quarters, thyme sprigs, rosemary sprigs, and garlic cloves in the chicken cavity.
Tie the legs together with kitchen twine and tuck the wings under the chicken.
In a small bowl, combine the olive oil, thyme, rosemary, minced garlic, salt, and pepper.
Rub the oil mixture all over the chicken skin to coat.
Place the prepared chicken in large roasting pan.
In a large mixing bowl, place all the prepared vegetables except the broccoli florets.
Add the olive oil, lemon juice, salt, and pepper, and mix until well combined.
Arrange the vegetables in the roasting pan around the prepared chicken.
Top with the sprigs of rosemary and roast for 12 minutes.
Reduce temperature to 350˚F and continue to roast for 45 minutes.
Add the broccoli florets and roast for a further 20 minutes, or until chicken is golden and cooked through and vegetables are tender. Chicken is cooked through when internal temperature registers at 165˚F.
Remove from oven and let rest for 10 minutes before cutting.