Preheat the oven to 350°F. Season the lamb shanks evenly on all sides with salt and pepper.
4 lamb shanks
Heat the oil in a large dutch oven or oven-safe pot set over medium-high heat. Working in batches if needed, sear the shanks for about 8 minutes total, turning to brown all sides. Transfer to a plate and set aside.
1 tablespoon extra virgin olive oil
Reduce the heat to medium. Add the shallots, carrots, and celery to the pot and cook, stirring occasionally, for 3-5 minutes, until softened. Add the garlic and cook for 30-60 seconds, stirring constantly, until fragrant.
Stir in the tomato paste and cook for 2-3 minutes, scraping the bottom of the pot and allowing the paste to darken slightly.
3 tablespoons tomato paste
Pour in the balsamic vinegar and stir to deglaze the pot. Add the stock, bay leaves, thyme, rosemary, lemon zest, salt, and pepper, then bring to a gentle simmer.
1/3 cup balsamic vinegar, 3 cups beef or chicken stock, 2 bay leaves, 2 teaspoons chopped fresh thyme leaves, 1 teaspoon chopped fresh rosemary, 1 strip lemon zest, 1/2 teaspoon kosher salt, 1/4 teaspoon ground black pepper
Return the lamb shanks to the pot, nestling them into the liquid and spooning some of the sauce over the top. Cover with a lid and transfer to the oven. Cook for 1 1/2 hours.
Remove the lid, turn the shanks, and return the pot to the oven uncovered. Continue cooking for about 1 hour, until the meat is very tender and beginning to pull away from the bone and the sauce has thickened slightly.
Serve the lamb shanks over warm polenta with plenty of sauce spooned over the top. Sprinkle with fresh thyme.
Polenta or mashed potatoes
Notes
Use a vegetable peeler to create the strip of zest, rather than grating with a microplane.