Pat the lamb pieces dry with paper towels and season generously with salt and black pepper on all sides. Finely dice the onion, carrots, and celery; mince the garlic; and crush the San Marzano tomatoes by hand over a bowl, keeping the juices.
Heat olive oil in a large Dutch oven over medium-high heat, then sear the lamb in a single layer (in batches if needed) for 3 to 4 minutes per side until deep golden brown on all sides. Transfer the browned lamb to a plate and set aside, leaving the drippings in the pot.
Reduce the heat to medium and cook the onion, carrots, and celery in the pot drippings for 8 to 10 minutes until softened. Add the garlic and cook for 2 minutes, then stir in the tomato paste and cook for 2 to 3 minutes until it darkens and smells fragrant.
Pour in the red wine and scrape up all the browned bits from the bottom of the pot. Simmer over medium-high heat for 3 to 4 minutes until the wine has reduced by about half and no longer smells of raw alcohol.
Add the crushed San Marzano tomatoes with their juices and the stock to the pot, then nestle the browned lamb back in. Tuck in the rosemary sprigs, thyme sprigs, and bay leaves, then sprinkle in the dried oregano and stir to combine. Bring to a gentle boil.
Reduce the heat to low, place the lid slightly ajar, and simmer gently for 2 to 2.5 hours, stirring every 30 minutes, until the lamb is completely fork-tender and falling apart. Remove the lid for the final 20 to 30 minutes if the sauce needs to reduce and thicken.
Transfer the lamb to a cutting board, discard the herb sprigs and bay leaves, and shred the lamb with two forks, removing any bones or large pieces of fat. Return the shredded lamb to the sauce, stir to combine, taste and adjust salt and pepper, then simmer uncovered for 5 to 10 more minutes.
Cook the pasta in heavily salted boiling water until al dente, reserve 1 cup of pasta water, then drain and toss the pasta directly in the ragu over medium heat, adding splashes of pasta water as needed to coat. Serve immediately topped with freshly grated Parmigiano-Reggiano and optional parsley.