In a large skillet, cook the ground lamb over medium heat until browned. Drain any excess fat.
Add the finely chopped onion and minced garlic to the skillet, and cook until softened, about 5 minutes.
Stir in the diced carrots and cook for another 5 minutes.
Add the tomato paste, Worcestershire sauce, beef or lamb broth, thyme, salt, and black pepper. Stir to combine.
Bring the mixture to a simmer and cook for about 20 minutes, or until the carrots are tender and the sauce has thickened.
Stir in the frozen peas and cook for an additional 5 minutes.
Transfer the filling to a baking dish and spread it out evenly.
While the filling is cooking, place the potatoes in a large pot and cover with water. Bring to a boil, then reduce the heat and simmer until the potatoes are tender, about 15-20 minutes.
Drain the potatoes and return them to the pot.
Add the milk and butter, and mash until smooth and creamy.
Season with salt and black pepper to taste.
Preheat your oven to 400°F (200°C).
Spread the mashed potatoes evenly over the filling in the baking dish, using a fork to create a decorative pattern on the surface.
Place the baking dish in the preheated oven and bake for about 20-25 minutes, or until the top is golden brown and the filling is bubbling.
Allow the Shepherd's Pie to cool slightly before serving.
Enjoy your meal!