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Take the chicken out of the fridge 30 minutes before cooking. Remove anything inside the cavity. Pat the chicken dry all over with paper towels — the skin should feel like paper. Preheat oven to 425°F.
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Mix softened butter with garlic powder, paprika, onion powder, thyme, and rosemary. Mash with a fork into a paste. Rub olive oil all over the chicken, then rub the herb butter everywhere — over the breast, legs, thighs, and under the breast skin. Season generously with salt and pepper. Tuck smashed garlic inside the cavity.
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Toss potatoes, carrots, and onion wedges with olive oil, salt, and pepper. Spread in a single layer in a large roasting pan. Set the chicken directly on top, breast side up.
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Roast for 1 hour without opening the oven. Check the temperature with a meat thermometer — you're looking for 165°F in the thickest part of the thigh. If not there yet, give it another 10-15 minutes.
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Remove from oven and let rest on a cutting board for 15 minutes before carving. Serve with the pan vegetables and drippings spooned over everything.