Boil potatoes in salted water until soft (about 15–20 minutes). Drain, mash with butter and milk, then set aside.
Cook lamb in a skillet with olive oil until browned.
Add onions and carrots. Cook 5–6 minutes until soft.
Stir in peas, tomato paste, Worcestershire sauce, thyme, salt, pepper, and broth. Simmer for 10 minutes until thickened.
Spread meat mixture in a baking dish. Top with mashed potatoes and smooth with a fork.
Bake at 375°F (190°C) for 20–25 minutes or until golden on top.
Let rest for 5 minutes before serving.