Heat a large skillet over medium heat and add the ground lamb. Cook until browned, breaking it up with a spoon as it cooks. Drain excess fat if needed.
Add the diced onion, carrots, and garlic to the skillet. Cook for 5 minutes until the vegetables soften.
Stir in the tomato paste, beef broth, Worcestershire sauce, and dried thyme. Simmer for 10 minutes until the mixture thickens slightly. Add the frozen peas and cook 2 more minutes. Season with salt and pepper.
While the filling simmers, place the cubed potatoes in a large pot and cover with water. Bring to a boil and cook until tender, about 15 minutes. Drain well.
Return the potatoes to the pot. Add the butter, milk, and shredded cheddar cheese. Mash until smooth and creamy. Season with salt and pepper to taste.
Preheat the oven to 400 degrees. Spread the meat filling evenly in a baking dish. Spoon the cheddar mashed potatoes over the top and smooth with a spatula.
Bake for 20 minutes until the topping is lightly golden. Let the dish rest for 5 minutes before serving.