01 - Preheat oven to 350°F.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Season lamb with salt and pepper; sear in batches until browned on all sides. Remove and set aside.
03 - In the same pot, add onion, carrots, celery, and garlic. Sauté for 5-7 minutes until softened.
04 - Stir in tomato paste; cook 1 minute. Deglaze with red wine, scraping up browned bits.
05 - Return lamb to pot. Add stock, Worcestershire sauce, thyme, rosemary, and bay leaves. Bring to a simmer. Cover and braise in the oven for 1 hour 30 minutes, or until lamb is fork-tender.
06 - Remove bay leaves. Stir in peas, parsnips, mushrooms, and extra carrots. Simmer uncovered on the stovetop for 10 minutes. If sauce is thin, sprinkle in flour and stir to thicken. Adjust seasoning.
07 - Meanwhile, cook potatoes in salted boiling water until tender, about 15-20 minutes. Drain, mash with butter and milk, and season with salt and pepper. Stir in Parmesan if desired.
08 - Transfer lamb and vegetable mixture to a large baking dish. Spread mashed potatoes evenly on top, creating peaks with a fork.
09 - Bake at 400°F for 25-30 minutes, or until the top is golden and filling bubbles at the edges. Rest for 10 minutes before serving.