Preheat your oven to 325°F (160°C).

Pat the lamb leg dry with paper towels. Season generously with salt and black pepper.

In a large, oven-safe pot or Dutch oven, heat olive oil over medium-high heat. Add the lamb leg and sear on all sides until browned, about 4-5 minutes per side. Remove the lamb and set aside.

In the same pot, add minced garlic, rosemary, and thyme. Sauté for 1-2 minutes until fragrant.

Pour in the balsamic vinegar and scrape the bottom of the pot to remove any browned bits. Allow the vinegar to simmer for 2-3 minutes.

Stir in the beef or lamb broth, Dijon mustard, and honey. Mix well to combine.

Return the lamb leg to the pot, ensuring it is submerged in the liquid. Cover with a lid and transfer to the preheated oven. Braise for 2.5 to 3 hours, or until the lamb is fork-tender.

Once the lamb is done, remove it from the pot and let it rest for 15 minutes. If you desire a thicker gravy, mix cornstarch with a small amount of water to create a slurry, then stir it into the pan juices. Simmer on the stovetop until thickened.

Slice the lamb and serve with the velvety pan gravy. Garnish with fresh herbs.