Preheat oven to 425 degrees. Place chicken, breast side up, on a baking sheet. Rub with 2 tablespoons oil; season generously with salt and pepper. Place parsley and 1 lemon half in cavity. Tie legs together with kitchen twine.
Toss potatoes and 2 tablespoons oil. Drizzle with juice from remaining lemon half. Season with salt and pepper. Scatter potatoes along chicken.
Roast for 15 minutes. Reduce temperature to 375 degrees; cook for 25 minutes. Rotate pan, toss potatoes, and cook until potatoes and chicken are golden brown and a thermometer inserted into the thickest part of the chicken's thigh reaches 165 degrees, about 25 minutes more. Let chicken and potatoes stand for 10 minutes.
Meanwhile, make the sauce: Combine ingredients. After 10 minutes, brush sauce on chicken and drizzle on potatoes.
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