Prepare the chicken: Pat the whole chicken thoroughly dry with paper towels. This is critical for crispy skin. Place the chicken breast side up on a clean cutting board. Using a sharp chef's knife, locate the keel bone and make a deep cut along one side of it, exposing the breast meat. Continue cutting down towards the thigh joint. Repeat on the other side of the keel bone. Separate the two breast halves from the carcass. Next, locate the thigh joint by feeling for the hip bone. Cut through the skin and down to the bone, then twist the leg until the joint pops. Slice through the joint to detach the thigh and drumstick. Repeat for the other leg. To separate the leg quarters, bend the thigh backward to break the skin and cartilage, then cut through the joint. Now, locate the wing joint where it meets the breast. Cut through the skin and joint to remove the wings. You should now have 8 pieces: 2 breasts (bone-in, skin on), 2 thighs, 2 drumsticks, and 2 wings. Trim any excess fat and cartilage from the pieces. Season all chicken pieces generously on all sides with kosher salt and freshly ground black pepper.

Roast the vegetables: Preheat oven to 400°F (200°C). In a medium bowl, toss the prepared root vegetables with olive oil, salt, and pepper. Spread in a single layer on a baking sheet.

Sear the chicken: Heat a large, oven safe skillet (cast iron is ideal) over medium high heat. Add 1 tablespoon of olive oil. Once the oil is shimmering, carefully place the chicken breasts, skin side down, into the hot skillet. Sear for 4-5 minutes, until the skin is deeply golden brown and crisp. Flip the chicken breasts and sear the other side for 2-3 minutes. Remove the chicken breasts from the skillet and set aside on a plate. Sear the leg quarters, skin side down, for 4-5 minutes until golden brown. Sear the wings for 2-3 minutes per side. Remove all chicken pieces from the skillet and arrange them on the baking sheet with the root vegetables, ensuring they are in a single layer and not overcrowding the pan.

Finish cooking: Place the baking sheet with the chicken and vegetables into the preheated oven. Roast for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) in the thickest part of the breast and thigh, and the vegetables are tender and caramelized. Remove from oven and let the chicken rest on a clean cutting board for 10 minutes before serving.

Make the pan sauce: While the chicken rests, return the skillet used for searing to medium heat. Add the 2 tablespoons of butter. Once melted, add the minced shallot and cook, stirring frequently, until softened and translucent, about 2-3 minutes. Add the minced garlic and cook for 30 seconds until fragrant, being careful not to burn it. Deglaze the pan by pouring in the white wine, scraping up any browned bits (fond) from the bottom of the skillet. Let the wine simmer and reduce by half, about 3-4 minutes. Pour in the chicken stock and bring to a simmer. Cook for another 5-7 minutes, allowing the sauce to thicken slightly. Stir in the fresh lemon juice, chopped parsley, thyme, and rosemary. Season the sauce with salt and pepper to taste.

Serve: Arrange the roasted root vegetables on serving plates. Place a rested chicken breast and a leg quarter (thigh and drumstick) on top of the vegetables. Spoon the lemon herb pan sauce generously over the chicken. Garnish with extra fresh herbs if desired.