Rinse chicken and remove giblets. Pat dry with paper towels.
Mix chicken rub ingredients in a small bowl and rub onto the chicken, both outside and inside. Stuff the chicken with rosemary, thyme and 2 lemon halves. Set the chicken aside.
In a 10-inch cast iron skillet, heat up olive oil over medium-high heat, about 2 minutes. Sauté onion for 2-3 minutes until fragrant. Stir in wine and cook until evaporates, about 3-4 minutes. Add broth, carrots and sliced lemon. Stir well and place the seasoned chicken on top.
Bake for 1.5 hours to 2 hours until chicken is completely cooked through and the temperature near the bones reaches 165°F. Baste the chicken with broth and juices a couple times during the roasting process.
Once chicken is done, transfer the chicken and the vegetables to a serving plate. Skim as much fat as possible from the surface of the remaining broth and juices in the skillet with a big spoon and bring it to a boil. Cook until the sauce is thickened, about 10 minutes. Season it with salt to taste.
Slice chicken, serve with vegetables and sauce.
If you would like to thicken the sauce more, dissolve 1 tablespoon cornstarch in 2 tablespoons cold water and add to the skillet when boiling. Stir until thickened.