In a large bowl combine Yukon gold potatoes, sweet potatoes, carrots and shallots and/or onion. Drizzle vegetables with half of the melted butter. Sprinkle with half of the salt and half of the pepper; toss gently to coat.
Rinse the chicken body cavity; pat dry with paper towels. Skewer neck skin of chicken to back. Place the one halved lemon in body cavity. Tie legs to tail. Twist wing tips under back. Place chicken, breast side up, on a rack in a shallow roasting pan. Brush chicken with the remaining melted butter.
In a small bowl, stir together lemon peel, parsley, rosemary, snipped fresh or dried thyme, minced garlic, the remaining salt and the remaining pepper; rub onto chicken. If you like, insert a meat thermometer into center of an inside thigh muscle. (The thermometer should not touch bone.) Place vegetables around chicken. If you like, add fresh thyme sprigs, garlic bulbs, and additional lemon halves.
Roast, uncovered, in a 375 degree F oven for 1-1/4 to 1-1/2 hours or until drumsticks move easily in their sockets and chicken is no longer pink (180 degrees), stirring vegetables once or twice. Remove chicken and vegetables from oven. Cover; let stand for 10 minutes before carving chicken.* Makes 4 to 5 servings.
If the vegetables are not done, return them to the oven while the chicken stands.