Preheat your oven to 325°F (160°C).

In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Rub the lamb shoulder with sea salt and black pepper, then sear it in the pot until browned on all sides, about 8-10 minutes. Remove the lamb and set aside.

In the same pot, add the chopped onion and sauté until translucent, about 5 minutes. Stir in the minced garlic and cook for another minute until fragrant.

Pour in the balsamic vinegar, scraping the bottom of the pot to deglaze. Add the chicken broth, honey, dried thyme, and fresh rosemary sprigs. Bring the mixture to a simmer.

Return the lamb shoulder to the pot, nestling it among the onions and garlic. Add the diced root vegetables around the lamb.

Cover the pot with a lid and transfer it to the preheated oven. Braise the lamb for about 3-4 hours, or until the meat is tender and falls off the bone.

Once cooked, remove the pot from the oven. If you prefer a thicker gravy, mix the cornstarch with a little water to create a slurry and stir it into the sauce over medium heat until thickened.

Serve the lamb shoulder with the root vegetables and drizzle with the balsamic glaze from the pot. Garnish with fresh rosemary sprigs.