1 cup best-quality red-wine vinegar
2 to 3 garlic cloves, minced (about 2 tablespoons)
3 sprigs of fresh rosemary (about 1 tablespoon minced)
5 1/2 pounds bone-in chicken pieces
Coarse salt and freshly ground black pepper
Extra-virgin olive oil
3/4 cup chicken broth, plus more as needed

At least 15 minutes and up to 2 hours before cooking, combine the vinegar, garlic, and rosemary to marinate. Thoroughly season the chicken pieces with salt and pepper. Heat a 14-inch skillet (or two smaller skillets) over high heat and swirl in enough olive oil to coat the bottom of the skillet. Place the chicken in the skillet, skin side down. Don’t crowd the chicken; leave space around each piece. Work in batches if necessary. You should hear an immediate sizzle when the chicken pieces hit the pan. Don’t move them; it takes a couple of minutes to sear the chicken so it doesn’t stick. Brown all sides; this will take 10 minutes per batch. Regulate the heat so it stays high but does not burn the chicken. Place all the browned chicken back in the skillet. Add the chicken broth and scrape up any brown bits from the bottom of the pan. Lower the heat, simmer, and reduce for 15 to 20 minutes. Increase the heat to high and pour in the vinegar mixture. Swirl the pan and stir around as the vinegar evaporates to form a simmering glaze, 8 to 10 minutes. Serve immediately or refrigerate, and reheat with some extra broth.