Step 1: Prepare the Chicken

1. Pat the chicken pieces dry with paper towels. Season them generously with salt and black pepper on all sides.
2. Lightly dredge the chicken in flour, shaking off any excess. The flour helps create a golden crust and thickens the braising liquid.

Step 2: Sear the Chicken

1. Heat 2 tablespoons of olive oil or butter in a large Dutch oven or heavy-bottomed skillet over medium-high heat.
2. Add the chicken, skin-side down, and sear for 4-5 minutes per side until golden brown. Do this in batches if necessary to avoid overcrowding the pan.
3. Transfer the seared chicken to a plate and set aside.

Step 3: Sauté the Vegetables

1. In the same pot, add the onion, carrots, and celery. Cook for 5-6 minutes over medium heat, stirring occasionally, until the vegetables are softened.
2. Add the minced garlic and cook for an additional 30 seconds until fragrant.

Step 4: Build the Braising Liquid

1. Deglaze the pot by pouring in the white wine (or chicken broth), scraping up any browned bits from the bottom of the pan with a wooden spoon.
2. Stir in the chicken broth, crushed tomatoes, tomato paste, thyme, rosemary, and bay leaves. Add the balsamic vinegar if desired. Bring the mixture to a simmer.

Step 5: Braise the Chicken

1. Return the seared chicken to the pot, nestling it into the braising liquid with the skin side up. The liquid should cover about two-thirds of the chicken, leaving the skin exposed to stay crispy.
2. Reduce the heat to low, cover the pot with a lid, and simmer gently for 40-50 minutes, or until the chicken is cooked through and tender.

Step 6: Adjust the Sauce

1. Remove the chicken from the pot and set it aside.
2. Increase the heat to medium-high and let the sauce simmer uncovered for 5-7 minutes to thicken slightly. Taste the sauce and adjust the seasoning with additional salt, pepper, or a splash of balsamic vinegar, if needed.

Step 7: Garnish and Serve

1. Return the chicken to the pot, spooning the sauce over the top. Sprinkle with freshly chopped parsley.
2. Serve the Rustic Braised Chicken hot with crusty bread, mashed potatoes, or buttered noodles to soak up the flavorful sauce.