In a roasting pan, lay out the carrots, potatoes, celery and, beets. Do your best to cut all the vegetables in a similar size.
Drizzle olive oil over the vegetables and add the zest of 1/2 a lemon, 6 sprigs of thyme, 1 spring of rosemary, season with salt and pepper. Toss to coat.
Place the chicken on top of the vegetables and pat dry with a paper towel (both in the cavity and on the skin).
Cut the lemon in quarters, place half of the lemon in the chicken cavity along with the last of the rosemary, garlic cloves, and thyme.
Cut half the butter into small squares and place under the skin, along with some salt and pepper.
Rub the remaining butter over the skin, along with two sage leaves (cut small), the leaves from one sprig of thyme, salt, and pepper.
Roast in the oven for 20-25 minutes, or until skin browns.
While the chicken roasts, melt the butter in a saucepan and add the salt and garlic. Let it simmer on low for 10 minutes, then turn off the burner and remove from heat.
Take out the chicken, turn down the heat to 400 and baste with the butter.
Cook the chicken for 60 minutes, basting once or twice, or until the chicken's internal temperature reaches 165F.
Remove the chicken from the oven and let rest for 10-15 minutes.
Optional steps
The vegetables will be soft from all that butter, the chicken juices, etc so pour the juices into a saucepan.
Place the vegetables back in the oven and roast until crispy.
I boiled down the juices and topped with some more garlic and a little white wine as a sauce to pour over the chicken.