Position a rack in your oven so that a Dutch oven or similar large, deep skillet can fit inside of it. Preheat the oven to 450°F.

In the Dutch oven or deep skillet, heat the oil over medium-high heat. Pat the chicken dry and season all over with the salt and pepper. Carefully place the chicken in the skillet skin-side down, arrange it so the thighs are not touching (you will probably need to cook them in 2 bathes). Cook until deeply golden, about 6 minutes, disturbing the chicken as little as possible (no need to brown the other side). Transfer to a plate. Repeat with remaining thighs.

Add the onion and carrot. Reduce the heat to medium and cook until the vegetables begin to soften, about 5 minutes.

Stir in the garlic, rosemary, and red pepper flakes, and let cook until fragrant, about 30 seconds.

Increase the heat back to medium-high. Pour in the wine. With a wooden spoon, scrape along the bottom of the skillet to remove any stuck on bits. Set simmer until reduced by approximately half, about 3 or so minutes.

Return the chicken to the skillet, along with any juices that have collected on the plate. Add enough chicken broth to come about halfway up the chicken. Increase the heat and bring the broth to a simmer.

Transfer the skillet to the oven and bake uncovered for 5 minutes at 450°F, then reduce the oven temperature to 325°F. Continue baking uncovered for 30 to 35 minutes more, until the thighs are super tender—a thin, sharp knife should insert effortlessly. Remove the skillet from the oven, then transfer the chicken thighs to a serving platter. Use a slotted spoon scoop the onion and carrot around the chicken (don't worry if there is still some onion left in the pan).

Bring the juices in the skillet to a simmer over high heat. Let simmer for about 5 minutes, until slightly thickened. Spoon some of the drippings over the chicken and vegetables, reserving the rest to add to more servings as desired (or sop the liquid gold up with bread). Sprinkle with fresh parsley, then enjoy hot.