First, stuff the cavity of the whole chicken with the quarters of apple and lemon. Truss the chicken fully, or just tie the legs together with kitchen twine. Mix together all of the ingredients for the Brown Sugar Coffee Rub and coat the chicken fully. This part might be a bit messy - don’t be scared to use your fingers. Place the prepared chicken on a plate and chill in the fridge uncovered for about an hour.
Preheat the oven to 400 degrees F. Grease an oven-safe dish just big enough to contain your bird with one tablespoon butter (I like to use a deep stoneware casserole dish, but a dutch oven or roasting pan are good choices as well).
Layer the squash, apple, and carrots in the bottom of the roasting dish. Top with sprigs of marjoram.
Remove the chicken from the fridge and place it on top of the bed of vegetables. Cut the remaining 2 tablespoons of butter into pieces and sprinkle them evening over the bird.
Roast in the oven for 45 minutes to an hour. The chicken is done when juices run clear and the internal temperature is 165 degrees F. The skin should get nice and crispy.