01 - Set the oven temperature to 400°F (200°C).
02 - Remove giblets from the chicken and pat the skin dry using paper towels.
03 - Rub the entire chicken with olive oil, then season evenly with kosher salt and black pepper.
04 - Place lemon halves, 4 sprigs of thyme, and 2 smashed garlic cloves inside the chicken cavity.
05 - Distribute the quartered onions, carrot chunks, remaining thyme sprigs, and smashed garlic in the roasting pan, creating a bed for the chicken.
06 - Place the chicken breast-side up on top of the vegetables. Tuck wing tips beneath the bird and tie the legs together with kitchen twine if desired.
07 - Cook for 1 hour and 15 minutes, basting one to two times with pan juices. If the pan dries out, add the optional white wine or chicken broth to maintain moisture.
08 - Verify that the juices run clear when the thigh is pierced or that the internal temperature reaches 165°F (74°C).
09 - Remove the chicken from the oven, loosely tent with foil, and let rest for 10 minutes before carving.
10 - Plate the carved chicken alongside the roasted vegetables and drizzle with pan juices.