Place the cubed white potatoes, sweet potatoes, and parsnips in a large pot. Cover with cold, salted water and bring to a boil. Reduce heat and simmer for 20–25 minutes, or until all vegetables are fork-tender.

Drain the vegetables well and return them to the pot over low heat for 1 minute to evaporate excess moisture. Mash the mixture using a potato masher or ricer. Add the softened butter, milk or cream, salt, and pepper. Mash and stir until the topping is smooth and creamy. Set aside.

Heat the olive oil in a large skillet over medium-high heat. Add the ground lamb and cook for 8–10 minutes, breaking it up with a spoon, until fully browned. Drain off any excess fat.

Add the diced onion, carrot, and celery to the lamb. Cook for 5–7 minutes until the vegetables soften. Stir in the minced garlic and cook for 1 minute until fragrant.

Sprinkle the flour over the meat and vegetables. Stir for 1 minute to cook the raw flour taste out. Stir in the tomato paste and cook for 1 more minute.

Pour in the beef stock. Add the Worcestershire sauce, rosemary, and thyme. Bring the mixture to a simmer, then reduce the heat to low. Simmer, uncovered, for 10 minutes until the sauce has thickened. Stir in the frozen peas and season with salt and pepper to taste.

Preheat oven to 400°F (200°C).

Pour the hot lamb filling into the prepared baking dish, spreading it into an even layer.

Spoon the root vegetable mash over the filling. Using a fork, gently spread the mash to cover the filling completely, smoothing it out. Then, use the tines of the fork to create small ridges and peaks across the surface—these will turn golden and crispy.

Bake for 25–30 minutes, or until the filling is bubbling up around the edges and the mash topping is golden brown and crisp.

Let the pie rest for 10–15 minutes before serving. This allows the gravy to settle and prevents it from spilling out when sliced.