In a large cooker (deeper frying pan with a lid), heat the oil over medium high heat. Salt and pepper the chicken. Place skin down into the cooker and brown for about 5 minutes, then flip it over and brown for another few minutes.
Add in the butternut squash, carrots, broth and about half of the rosemary. Salt and pepper some more. Lower heat to medium high and cover for 20 minutes.
After 20 minutes, add the rest of the ingredients. You can add a bit more salt and pepper. Make sure that there is still a bit of broth in the cooker. If not, add just a bit more. It will make the chicken nice and tender, and will give you a nice gravy-like sauce at the end. Cover and cook for another 15-20 minutes.