Preheat oven to 150°C. Pat lamb dry, season heavily.
Heat olive oil in a heavy oven-safe pot. Brown lamb in 3 batches, 4 minutes per batch. Set aside.
Reduce heat to medium. Add onion, carrot, celery, cook 8 minutes. Add garlic and anchovies, mash anchovies into the soffritto. Cook 2 minutes.
Add tomato paste, stir into the dry pan for 90 seconds until darkened.
Pour in wine, scrape the base, reduce by half. Add tomatoes, stock, rosemary, bay leaf and the lamb.
Cover and braise in the oven for 2.5 hours until the lamb falls apart at the suggestion of a fork.
On the stovetop, pull the lamb into rough strands using two forks directly in the pot. Simmer uncovered for 15 minutes to reduce.
Cook pappardelle in heavily salted boiling water for 3 minutes. Reserve a cup of pasta water. Drain.
Toss pasta through the ragu in the pot, adding pasta water as needed to loosen. Off the heat, fold through half the parmigiano and most of the mint.
Serve in warm bowls topped with the remaining parmigiano and mint, and a hard crack of pepper.