Rinse chicken and pat dry with paper towels. Place on rack in roasting pan. Insert lemon halves and fresh thyme into cavity. Arrange carrots and mushroom caps around pan and add about 1-inch of chicken broth. You can use butcher's twine to tie the legs together in front (or not, completely optional).
In a skillet over medium heat add 1 Tbl. butter and sauté sage and thyme leaves for 3-4 minutes, then add chopped mushrooms and shallot. Saute until tender and mushrooms have released their liquid, about 10 minutes. Season mixture with salt and pepper to taste. Allow to cool slightly.
Preheat oven to 425 degrees.
Loosen chicken skin above breasts and using hands, tuck mushroom mixture evenly under skin. Then coat the outside of the chicken with olive oil.
Combine spice rub ingredients; using hands coat entire chicken with seasoning.
Preheat oven to 425 degrees.
Bake at 425 degrees for 30 minutes or until nicely browned. Baste chicken with broth from pan. Reduce oven temperature to 350 degrees and loosely tent chicken with foil. Continue baking for an additional hour or until chicken is done (juices run clear and thermometer inserted into the inner thigh registers 165 degrees). If your chicken comes with a pop-up timer trust it.
Once done, allow chicken to rest at least 15 minutes before carving. Don't forget to reserve the carcass for making homemade chicken broth.
