01 - Preheat the oven to 375°F.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Brown the lamb cubes on all sides in batches, then set aside.
03 - Add onion, carrots, and celery to the same pot. Sauté until softened, about 5 minutes. Add garlic and cook 1 minute more.
04 - Stir in tomato paste and cook for 2 minutes. Deglaze with red wine, scraping up browned bits from the bottom. Simmer until reduced by half, 3–4 minutes.
05 - Return lamb to the pot. Add stock, thyme, bay leaf, salt, and pepper. Bring to a boil, then lower heat, cover, and simmer gently for 1 hour, stirring occasionally.
06 - Remove bay leaf. Stir in peas, parsnips, mushrooms, and Worcestershire sauce. Simmer uncovered for 10–15 minutes until vegetables are tender and sauce has thickened. Adjust seasoning as needed.
07 - Boil potatoes in salted water until fork-tender, about 15–20 minutes. Drain well.
08 - Mash potatoes with butter, warmed milk, salt, and white pepper until smooth. Stir in Parmesan if using.
09 - Spoon lamb and vegetable mixture into a 9x13-inch baking dish. Spread mashed potatoes evenly over the top, using a fork to create textured peaks.
10 - Bake for 30–35 minutes until filling is bubbling and potatoes are golden. For extra browning, broil for 2–3 minutes at the end.
11 - Let rest for 10 minutes before serving.