Preheat your oven to 400°F (200°C).
In a large skillet over medium heat, add the ground lamb and cook until browned, breaking it apart with a spoon. Drain excess fat if necessary.
Add the chopped onion, diced carrots, and minced garlic to the skillet. Sauté for about 5 minutes, or until the vegetables are softened.
Stir in the tomato paste, beef broth, Worcestershire sauce, dried thyme, salt, and pepper. Bring the mixture to a simmer and cook for 10 minutes to thicken the sauce.
Add the frozen peas and stir to combine. Remove the skillet from heat.
Transfer the meat mixture to a baking dish and spread it out evenly.
Top with the prepared mashed potatoes, spreading them to cover the meat completely. Use a fork to create texture on top.
Dot the top with butter and sprinkle with shredded cheddar cheese if desired.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and the filling is bubbling.