Preheat oven to 425°F (220°C). Pat the chicken completely dry with paper towels, then rub all over — including under the breast skin — with 3 tbsp olive oil. Season generously inside and out with 1½ tsp salt and ½ tsp black pepper.
Stuff the cavity with the lemon halves, smashed garlic, thyme, and rosemary. Tie the legs together with kitchen twine and tuck the wing tips under the body.
Toss the halved potatoes with 2 tbsp olive oil, the remaining smashed garlic, and ½ tsp salt. Scatter them in a single layer in a roasting pan or oven-safe skillet.
Set the chicken breast-side up on top of the potatoes. Roast for 1 hour to 1 hour 15 minutes, until a thermometer in the thickest part of the thigh reads 165°F (74°C) and the skin is deep golden brown.
Transfer the chicken to a cutting board and tent loosely with foil. Rest for 10-15 minutes so the juices redistribute, then carve and serve with the roasted potatoes.
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