Start by patting the chicken thighs completely dry. In a bowl, toss the thighs with 1 tbsp of olive oil, plus a generous amount of salt, pepper and the chopped rosemary leaves.
Heat the remaining 1 tbsp of olive oil in a large, heavy-bottomed pan or Dutch oven over medium-high heat. Lay the seasoned chicken pieces in the hot oil, skin-side down, and sear for 5 to 7 minutes until the skin turns a deep, rich golden brown.
Turn the chicken over. Arrange the prepared carrots, garlic and onions, along with the whole rosemary sprigs, around the pieces. Pour the white wine over the vegetables and into the base of the pan.
Cover the pan with a lid, reduce the heat setting to low, and let thedish gently simmer for 45 minutes. The chicken is ready when it is completely tender and pulls easily from the bone (it should reach an internal temperature of 165°.
Transfer the finished chicken and vegetables to a platter. Spoon the rich pan juices over the top before serving immediately, ideally with some rustic bread to dip into the sauce.