Prep the chicken: Remove the chicken from the fridge 30-45 minutes before roasting. Pat it completely dry inside and out with paper towels — dry skin is the secret to crispiness. Season the cavity generously with salt and pepper, then stuff with the halved lemon, onion quarters, rosemary sprigs, and thyme sprigs.
Make the herb butter: In a small bowl, mash together the softened butter, garlic, chopped rosemary, thyme leaves, lemon zest, 1 tablespoon salt, and the pepper.
Butter the bird: Gently loosen the skin over the breast and thighs with your fingers. Push about two-thirds of the herb butter under the skin, spreading it evenly. Rub the remaining butter all over the outside of the chicken, then drizzle with olive oil.
Truss (optional but helpful): Tie the legs together with kitchen twine and tuck the wing tips under the body for even cooking.
Roast hot, then lower: Place the chicken breast-side up on a rack in a roasting pan (or on top of the potatoes and carrots tossed with oil and salt). Roast at 425°F (220°C) for 15 minutes, then reduce to 375°F (190°C) and roast 1 hour to 1 hour 15 minutes more, until the thickest part of the thigh reads 165°F (74°C) on an instant-read thermometer and the juices run clear.
Rest: Transfer the chicken to a cutting board and rest for 15-20 minutes. This redistributes the juices — don't skip it.
Carve and serve: Carve the chicken, spoon the pan juices over the meat, and serve with the roasted vegetables.