In either a large cast-iron skillet or oven-safe baking dish, create a base with your poatoes, carrots, celery, and 1 onion. Drizzle about 1/3 C of olive oil over the top, and sprinkle salt and pepper as desired. Mix well and place half of your sage and rosemary on top
In a small bowl, mix about 1/3 C olive oil, salt and pepper, garlic, rosemary, and thyme. Set aside
Cut the stick of butter into thirds and set one third aside in a separate microwave-safe bowl
With the two remaining chunks of butter, mix in the remaining rosemary and thyme and flatten the two pieces of herbed butter
Pat your chicken dry and remove any innerds. Rub the olive oil and herb mixture over the whole bird. Fill the cavity with the remaining onion, lemon, sage leaves, and rosemary sprigs. Then gently create two pockets between the skin and the meat on the breast, just above the cavity. Slide an herbed butter slab into each cavity. Tie the chicken legs together with twine
Place the chicken on top of the vegetable in the pan. Melt your remaining butter until it is melted, and then dip your cheesecloth in until it is fully coated. Tuck this around your bird to prevent it from drying out
Bake at 400° F for at least 90 minutes, or until the breast is cooked to 180° and the thighs are 190°. At 90 minutes, remove the cheesecloth so that the skin can brown and crisp up. If the wings are looking significantly more browned, you can cover them with foil so that they dont burn