Place peeled and cubed potatoes in a large pot and cover with cold salted water. Bring to a boil over high heat, then reduce to a steady simmer. Cook for 15–18 minutes until completely tender and easily pierced with a fork.

Drain the potatoes thoroughly, then return them to the hot pot for 1–2 minutes over low heat to evaporate any remaining moisture. This step ensures a fluffy, not gluey, mash.

Mash the potatoes with butter and warm milk until smooth and creamy. Season generously with salt and white pepper. Stir in the egg yolk if using. Set aside.

Preheat your oven to 400°F (200°C).

Heat olive oil in a large oven-safe skillet or sauté pan over medium-high heat. Add the diced onion, carrots, and celery. Cook for 5–6 minutes, stirring occasionally, until softened and beginning to turn golden.

Add the minced garlic and cook for 1 minute more until fragrant.

Add the ground lamb to the pan. Break it apart with a wooden spoon and cook over medium-high heat, undisturbed for the first 2–3 minutes to develop a proper sear. Continue cooking and breaking up the meat until fully browned, about 8–10 minutes total. Drain excess fat if needed, leaving about 1 tablespoon in the pan.

Stir in the tomato paste and cook for 2 minutes until it darkens slightly and coats the meat and vegetables.

Add the Worcestershire sauce, fresh rosemary, fresh thyme, salt, and pepper. Stir to combine.

Pour in the beef broth and stir, scraping up any browned bits from the bottom of the pan. Bring to a gentle simmer and cook for 8–10 minutes until the liquid has reduced by about half and the filling is thick and glossy. Taste and adjust seasoning.

Remove from heat and stir in the frozen peas.

Transfer the filling to a 9x13-inch baking dish (or keep it in the oven-safe skillet if using one). Spread it into an even layer.

Spoon the mashed potatoes over the filling and spread into an even layer using a spatula, making sure to seal the edges. For a decorative finish, use a fork to create ridges or use a piping bag to pipe the potatoes on top.

Bake at 400°F for 20–25 minutes until the edges are bubbling and the potato topping is set.

Switch the oven to broil and broil for 3–4 minutes until the peaks of the mashed potato topping turn golden brown. Watch carefully — it can go from golden to burnt quickly.

Remove from the oven and let the pie rest for 5–10 minutes before serving. This helps the filling set slightly so it scoops cleanly onto plates.