Preheat the oven to 175°C (350°F). 

Generously season the lamb shoulder with salt and pepper. In an oven-safe Dutch oven or heavy-bottomed pot, heat a drizzle of olive oil over medium-high heat. Brown the lamb for 2 to 3 minutes on each side, working in batches if necessary. Remove the meat and set aside. 

In the same pot, add the onion, carrots, and celery. Cook over medium heat for 3 to 4 minutes, stirring occasionally. Add the garlic and continue cooking for another 30 seconds. 

Pour in the fig balsamic vinegar and scrape the bottom of the pot to release the browned bits (fond). Let the liquid reduce until it has almost completely evaporated. 

Add the grainy mustard, crushed tomatoes, and beef broth. Mix well. Return the lamb to the pot. Add the bay leaves, rosemary, dried mint, and dried oregano. Cover. 

Place in the oven for about 2½ hours, or until the lamb is very tender and easily falls apart when tested with a fork. Turn the meat over halfway through cooking, if necessary. 

Remove the bones, bay leaves, and rosemary sprigs. Shred the meat using two forks. Stir everything together and adjust the seasoning if needed. Add the fresh chopped parsley and Parmesan cheese. 

Towards the end of the stew’s cooking time, bring a large pot of generously salted water to a boil. Cook the pappardelle according to the package instructions until al dente. Before draining, reserve about 250 ml (1 cup) of the pasta cooking water. 

Add the drained pappardelle to the pot. Gradually stir in some of the reserved cooking water—starting with about 125 ml (½ cup)—until the sauce coats the pasta generously. 

Divide among warm plates and top generously with freshly grated Parmesan, a little parsley, and, if desired, a drizzle of olive oil.