Peel and chop the potatoes. Boil them in salted water until fork-tender, about 15–20 minutes.
Drain the potatoes and mash with butter, milk, salt, and pepper until creamy. Set aside.
Heat olive oil in a large skillet over medium heat. Brown the ground lamb, breaking it apart as it cooks.
Add onion and carrots and cook for 5–7 minutes until softened.
Add garlic and cook for about 30–60 seconds.
Stir in tomato paste, broth, Worcestershire sauce, thyme, rosemary, salt, and pepper.
Simmer for 8–10 minutes until the sauce thickens slightly.
Stir in the peas and cook for another 2–3 minutes.
Preheat the oven to 400°F (200°C).
Transfer the meat mixture to a baking dish and spread the mashed potatoes evenly over the top.
Use a fork to create ridges across the potatoes.
Bake for 20–25 minutes, until hot and golden on top.
Let the shepherd’s pie rest for 5–10 minutes before serving.