Preparation Stir 6 tablespoons salt, sugar, and 4 cups water in a large pot until salt and sugar dissolve. Add 4 more cups cold water. Add chicken. Cover, chill, and let brine for 4-12 hours. Preheat oven to 400°F. Set a wire rack inside a roasting pan. Remove chicken from brine; pat dry. Let sit for 20 minutes. Season lightly with salt. Heat 1 tablespoon oil in a large cast-iron skillet over medium-high heat. Arrange leg pieces, skin side down, in skillet. Place 1 head of garlic, cut side down, in center of skillet. Tuck 5 sprigs each of thyme and rosemary around chicken. Cook until skin is golden brown, 10-12 minutes. Transfer herbs and garlic on prepared rack. Add 1 tablespoon butter to skillet; swirl to coat. Flip chicken; baste with pan juices. Transfer, skin side up, to prepared rack. Repeat with 1 tablespoon oil, chicken breasts, 1 head of garlic, 5 thyme sprigs, 5 rosemary sprigs, and 1 tablespoon butter. Reserve drippings in skillet. Transfer chicken to oven and roast until an instant-read thermometer inserted into thickest part of thigh registers 160°F, about 20 minutes. Transfer chicken, herbs, and garlic to a platter. Let rest for 15 minutes. Meanwhile, heat drippings over medium heat, adding 1 tablespoon oil if dry. Add remaining herbs and garlic, cut side down. Stir until aromatic, 3-4 minutes. Add 2 tablespoons butter; stir until butter browns, 1-2 minutes. Squeeze lemon over. Pour over chicken.
Preparation Stir 6 tablespoons salt, sugar, and 4 cups water in a large pot until salt and sugar dissolve. Add 4 more cups cold water. Add chicken. Cover, chill, and let brine for 4-12 hours. Preheat oven to 400°F. Set a wire rack inside a roasting pan. Remove chicken from brine; pat dry. Let sit for 20 minutes. Season lightly with salt. Heat 1 tablespoon oil in a large cast-iron skillet over medium-high heat. Arrange leg pieces, skin side down, in skillet. Place 1 head of garlic, cut side down, in center of skillet. Tuck 5 sprigs each of thyme and rosemary around chicken. Cook until skin is golden brown, 10-12 minutes. Transfer herbs and garlic on prepared rack. Add 1 tablespoon butter to skillet; swirl to coat. Flip chicken; baste with pan juices. Transfer, skin side up, to prepared rack. Repeat with 1 tablespoon oil, chicken breasts, 1 head of garlic, 5 thyme sprigs, 5 rosemary sprigs, and 1 tablespoon butter. Reserve drippings in skillet. Transfer chicken to oven and roast until an instant-read thermometer inserted into thickest part of thigh registers 160°F, about 20 minutes. Transfer chicken, herbs, and garlic to a platter. Let rest for 15 minutes. Meanwhile, heat drippings over medium heat, adding 1 tablespoon oil if dry. Add remaining herbs and garlic, cut side down. Stir until aromatic, 3-4 minutes. Add 2 tablespoons butter; stir until butter browns, 1-2 minutes. Squeeze lemon over. Pour over chicken.