Dry the chicken: Take the chicken out of the fridge 30 to 45 minutes before it goes in the oven. Pull out the giblets and pat the bird very dry inside and out with paper towels. Dry skin is crisp skin, and this is the least glamorous step that matters most.

Make the herb butter: Heat the oven to 425°F with a rack in the lower third. Mash the softened butter with the minced garlic, chopped rosemary, thyme leaves, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper until it's evenly green and speckled.

Get the butter under the skin: Slide your fingers between the skin and the breast meat to loosen it, working back toward the thighs without tearing anything. Push about two thirds of the butter underneath and spread it around from the outside, then smear the rest over the skin. Season the bird all over with the remaining 2 teaspoons salt and 1/2 teaspoon pepper.

Stuff and tie: Put the lemon halves, halved garlic head, and thyme sprigs in the cavity. Tie the legs together with kitchen twine and tuck the wing tips underneath the bird so they don't burn.

Build the pan: Toss the potatoes, carrots, and onion with the olive oil in a roasting pan or large ovenproof skillet and spread them out. Set the chicken breast side up right on top of the vegetables.

Roast: Roast for 75 to 90 minutes, stirring the vegetables once about halfway through, until the skin is deep golden and a thermometer pushed into the thickest part of the thigh without touching bone reads 165°F. If the breast is browning faster than the legs are cooking, tent it loosely with foil.

Rest, then carve: Move the chicken to a cutting board and let it rest 15 minutes uncovered while the vegetables finish in the pan. Carve it, then spoon the pan juices over the meat and vegetables before they go to the table.