Preheat the oven to 325°F (160°C).
Season the lamb shanks with salt and pepper.
Heat olive oil in a Dutch oven over medium-high heat.
Sear the lamb shanks on all sides until beautifully browned, about 8-10 minutes.
Remove the shanks and set aside.
Add chopped onion, minced garlic, carrots, and celery to the pot.
Sauté for about 5 minutes until softened.
Stir in fig preserves, balsamic vinegar, beef broth, and dried thyme.
Return the lamb shanks to the pot, ensuring they are nestled in the sauce.
Bring everything to a simmer before covering and transferring it to the oven.
Braise for 2 to 2.5 hours or until the meat is fork-tender.
Remove the pot from the oven and let the shanks rest for 10 minutes before serving.
Serve with the glaze spooned over the top.