Preheat your oven to 325°F (160°C).

In a large Dutch oven, heat the olive oil over medium-high heat. Season the lamb shoulder with salt and pepper, then sear it in the pot until browned on all sides, about 5-7 minutes per side. Remove the lamb and set aside.

In the same pot, add the chopped onion, carrots, parsnips, and celery. Cook for about 5-6 minutes, or until the vegetables begin to soften.

Stir in the minced garlic, fresh tarragon, and dried thyme. Cook for an additional 2 minutes until fragrant.

Pour in the balsamic vinegar and scrape the bottom of the pot to deglaze. Add the tomato paste and mix well.

Return the lamb shoulder to the pot and pour in the stock. The liquid should come about halfway up the side of the lamb. Bring to a simmer.

Cover the pot with a lid and transfer it to the preheated oven. Braise for 3-4 hours, or until the lamb is tender and easily pulls apart with a fork.

Once the lamb is done, remove it from the pot and let it rest for 10-15 minutes. Meanwhile, place the pot with the gravy on the stove over medium heat.

Skim off any excess fat from the surface of the gravy. Simmer the gravy for about 10 minutes to thicken slightly. Adjust seasoning with salt and pepper to taste.

Slice or shred the lamb shoulder and serve it on a platter. Spoon the rich root vegetable gravy over the lamb and garnish with fresh tarragon. Enjoy!