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Place the top oven rack in the center position and pre-heat the oven to 400°F. Zest one of the lemons with a microplane and cut the rest of it into quarters. Set the zest and lemon aside.
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Slice the remaining lemon into ¼-inch thick slices and arrange on the bottom of a large, oven-safe skillet, along with the sliced yellow onion. Set aside.
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In a small bowl, combine 2 tablespoons of olive oil with the lemon zest, butter, garlic powder, onion powder, and Herbes de Provence. Season with salt and black pepper, to taste, and stir with a fork to create a paste.
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Place the chicken on top of the onions and lemon in the skillet and gently massage 1-2 tablespoons of the lemon-butter mixture under the skin. Spread the remaining mixture all over the outside of the chicken in an even layer.
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Stuff the chicken with the quartered lemon and 1/3 of the rosemary sprigs. Secure the legs together with kitchen string.
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In a large glass bowl, toss the baby red potatoes with the remaining olive oil and fresh rosemary. Season with salt and black pepper, as desired.
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Nestle the seasoned potatoes around the chicken before adding the chicken broth and whole peppercorns. Place the skillet in the pre-heated oven to roast for one hour.
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After an hour, remove from oven and check for doneness by inserting an instant-read thermometer between the leg and breast, but not against the bone.
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Note: Chicken should reach an internal temperature just below 165°F before removing from the oven. The temperature will rise several degrees as it rests.
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Let the chicken rest for 5-10 minutes before carving. Serve immediately topped with some of the juices from the skillet and the roasted rosemary potatoes on the side. Enjoy!