Heat olive oil in a skillet, sauté onions and carrots for 5 minutes.
Stir in garlic, then add ground lamb and cook until browned. Drain excess fat.
Mix in tomato paste, Worcestershire sauce, herbs, salt, and pepper. Add broth and simmer 10 minutes.
Stir in frozen peas and cook 2 minutes. Remove from heat.
Meanwhile, boil potatoes until fork-tender, about 15 minutes. Mash with butter, milk, and salt until creamy.
Preheat oven to 400°F (200°C). Spread meat mixture in a baking dish. Top with mashed potatoes and smooth evenly.
(Optional) Rough up surface with a fork and sprinkle with cheese.
Bake 20–25 minutes until golden brown. Cool slightly before serving.