Put the potatoes and carrots in a medium pot, cover with 1 inch of water and season with salt. Bring to a boil over high heat, then immediately drain and set aside.
Meanwhile, sprinkle the chicken with salt and black pepper. Melt the butter in a Food Network™ 13-in. Pre-Seasoned Cast-Iron Skillet over medium-high heat. Add the chicken skin-side down and the garlic cut-side down. Cook until both are golden brown, about 6 minutes. Transfer the chicken to a plate.
Add the potatoes, carrots and lemon to the skillet and cook, stirring occasionally, until the potatoes start to brown, about 6 minutes. Sprinkle with the red pepper flakes, 1 teaspoon salt and some pepper. Put the chicken on top of the vegetables skin-side up and roast in the oven until the chicken registers 165 degrees F on an instant-read thermometer and the potatoes are golden, about 20 minutes. Sprinkle with the parsley before serving.
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