Preheat oven to 400°F (200°C).
Place potatoes in a large pot, cover with cold salted water, and bring to a boil.
Cook for 15–20 minutes until fork-tender. Drain and set aside.
Heat olive oil or butter in a large skillet over medium heat.
Add ground lamb and cook until browned, breaking it up as it cooks.
Stir in onion and carrots. Cook 5–6 minutes until softened.
Add garlic and cook for 30 seconds until fragrant.
Stir in tomato paste and flour; cook for 1 minute.
Pour in broth and Worcestershire sauce. Add thyme, salt, and pepper.
Simmer 8–10 minutes until thick and saucy.
Stir in peas and remove from heat.
Mash potatoes with butter, milk or cream, salt, and pepper until smooth.
Spread meat filling evenly into a baking dish.
Top with mashed potatoes, spreading evenly and roughing up the surface with a fork.
Bake uncovered for 25–30 minutes until golden.
Let rest for 10 minutes before serving.