1. If you can, generously season your lamb shoulder all over with fine sea salt the night before you plan to cook it. My general rule of thumb with a large cut of meat is 1 teaspoon of fine sea salt per pound. Place the salted lamb shoulder on a wire rack lined quarter sheet tray for at least 30 minutes, or up to 24 hours in the fridge if you’re able to season in advance.
2. Preheat your oven to 325°F. Bring your lamb shoulder to room temperature before cooking.
3. Heat The Dutchess over medium-high heat. When quite hot but not smoking, place the lamb shoulder fat side down in the dutch oven. Sear on all sides until nicely browned, about 5 minutes per side. Transfer the lamb back to the wire rack.
4. Place the shallots and garlic cut side down in the pan and sear until golden, 3-5 minutes. Push the alliums towards the side to create space for the lamb, then nestle the lamb shoulder in the center. Add the wine and bay leaves. Bring the wine to a simmer, and cook for 5 minutes. Add 2 cups of filtered water, return to a simmer, then place the lid on the dutch oven and transfer it to the oven. Cook for 2 hours, checking once or twice to make sure the liquid isn’t evaporating too quickly.
5. At the 2 hour mark, add the quince and increase the oven temperature to 350°F. Nestle it around the lamb and submerge it as best you can in the braising liquid. If the liquid level is looking low, add another half cup to a cup of water. Season with a pinch of salt and return the pot to the oven, uncovered, for another 30 minutes — or until the meat is browned, crispy, and barely holds together when prodded with a fork. The quince should be soft and fudgy but not lifeless. Remove the pot from the oven and dunk the rosemary into the hot liquid to infuse for at least 5 minutes.