Preheat oven to 450f and set rack to middle level.
Dry off the chicken very well with paper towels both on both the outside and inside of the bird. Place the chicken into a roasting pan with a wire rack insert. Drizzle the melted butter and olive oil all over the chicken. Use your hands and get it all over.
Season the inside of the chicken with 1 teaspoon of kosher salt and the outside with the remaining salt. Season all over with pepper and rub in the herbs and the garlic as well. Try to get the seasonings under the skin as well as on top. Place the cut head of garlic inside the chicken's cavity.
Tie the legs together with kitchen twine and tuck the wing tips under the chicken.
Roast the chicken "breast" side down for 30 minutes then flip over to breast side up and baste with the pan juices. Return chicken to the oven and continue cooking until the temperature reaches 160f in the deepest part of the breast (about 30 more minutes). For more color broil the top for the last 1-2 minutes if desired.
Tent the chicken with foil and allow it to rest for 15 minutes prior to slicing to lock in the juices.
The exact cooking time will vary based on the size of the chicken. An internal temperature of 160f into the deepest part of the breast is fully cooked.
If you want to use the pan juices for gravy or a pan-sauce, use garlic powder instead of fresh garlic. Fresh garlic will burn after an hour of cooking.
Leftovers can be saved in the fridge for up to 3 days and can be reheated in the oven or microwave.