Source: Roast Chicken and Vegetables, Bride & Groom First and Forever Cookbook
3 carrots, cut into thirds
6 small red new potatoes, quartered if large
1 medium yellow onion, cut into 6 wedges
3 tablespoons unsalted butter, melted, or olive oil
Kosher salt and freshly ground pepper
1 chicken (3 to 4 pounds)
1 lemon, quartered
2 fresh rosemary sprigs
4 cloves garlic, peeled and smashed
Preheat the oven to 425 degrees F.
Put the carrots, potatoes, and onion in a 9-by-13-inch glass baking dish. Toss the vegetables with 1 tablespoon of the butter. Season with kosher salt and pepper to taste. Spread the vegetables to the edges of the baking dish, making room for the chicken.
Remove the neck and giblets from the cavity of the chicken and discard. Rinse the bird under cold running water and pat dry. Put the chicken, breast-side up, in the center of the baking dish. Brush the chicken with the remaining 2 tablespoons butter. Season the cavity and skin generously with kosher salt and pepper to taste. Put the lemon quarters and rosemary sprigs inside the cavity. Put the garlic cloves under the chicken to prevent them from burning.
Roast for 45 minutes. Remove the dish from the oven. Using tongs, tilt the chicken, pouring the juices from the cavity onto the vegetables, and shake to coat. Baste the chicken with the pan juices. If the bird is browning too quickly, cover with aluminum foil. Continue roasting until the chicken is a deep golden brown and the juices run clear when the tip of a knife is inserted into the thigh joint, or until an instant-read thermometer inserted into the thigh, away from the bone, registers 170 to 175 degrees F, 25 to 30 minutes more.
Transfer the chicken to a platter, cover loosely with aluminum foil, and let stand for 10 to 15 before carving. Using the back of a spoon, mash the garlic and squeeze some lemon into the pan juices. Toss the juices with the vegetables. Carve the chicken and serve the vegetables alongside. Drizzle any remaining juices over the chicken.