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1
Adjust oven racks to upper-middle and lower-middle position and preheat oven to 400°F. Heat 12-inch cast iron skillet in oven for 15 minutes.
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2
In large bowl, stir grated garlic, rosemary, zest, salt, pepper flakes, and 1 tablespoon oil. Add chicken pieces and toss to coat. Cover and let sit for 30 minutes.
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3
Meanwhile, place butter in cast iron skillet and return to oven until melted, about 2 minutes. Add potatoes, garlic, rosemary, and salt, and stir to coat. Spread potatoes out into single layer and place on lower-middle rack. Roast for 30 minutes. Remove potatoes, toss with a spoon to turn and coat with butter, then return to upper-middle rack.
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4
When potatoes have been transferred to upper-middle rack, prepare the chicken. Heat remaining tablespoon oil in 12-inch skillet over medium heat. Add chicken pieces, skin side down, and cook until well browned, 5 to 8 minutes. Reserve any lemon-rosemary mixture left in the chicken marinating bowl.
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5
Using tongs, turn chicken pieces over. Add carrots and remaining lemon-rosemary mixture to pan, and transfer to lower-middle rack in oven.
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6
Continue roasting until potatoes are fully cooked and golden and carrots are tender, about 25 minutes longer. As cooking time approaches end, check chicken pieces for doneness with an instant-read thermometer, removing chicken pieces as they finish cooking (155u00b0F for breast meat, 170u00b0F for legs and drumsticks), and keeping them warm on a plate covered in heavy duty foil. Serve potatoes and carrots with cooked chicken pieces.