Sauté aromatics: Heat olive oil in a large skillet. Sauté onions and garlic over medium heat until fragrant and golden, about 5 minutes.
Brown the lamb: Add ground lamb, breaking it up with a spoon. Cook until browned, letting the juices develop rich flavors.
Add veggies: Stir in carrots, tomato paste, and Worcestershire sauce. Pour in the broth, and let it simmer until thickened, about 10 minutes.
Season to perfection: Add frozen peas during the last 2 minutes of simmering. Season with salt and pepper to taste.
Boil potatoes: In a separate pot, boil potatoes for 15 minutes until fork-tender. Drain and return to the pot.
Mash it up: Add milk and butter to the potatoes. Mash until smooth and creamy. Stir in cheese for extra richness, if desired.
Assemble the pie: Spread the lamb mixture evenly in a baking dish. Top with mashed potatoes, smoothing the surface with a spatula.
Bake: Preheat oven to 400°F (200°C). Bake for 20 minutes or until the top is golden brown and crispy.
Serve: Garnish with fresh thyme for a touch of elegance. Serve hot and watch it disappear from plates.