1Preheat oven to 400°F. Bring a pot of salted water to boil and add potatoes. Cook 15–18 minutes until tender, then drain and return to pot.
2Meanwhile, heat a large skillet over medium-high. Brown the ground beef or lamb, breaking it up as it cooks, about 5 minutes. Drain excess fat if needed.
3Add diced onion, carrot, and celery to the meat. Cook 5 minutes until softened.
4Stir in garlic and cook 1 minute. Add tomato paste and stir for 1 minute.
5Pour in beef broth and worcestershire sauce. Add thyme, salt, and pepper. Simmer 5 minutes.
6Fold in frozen peas and cook 2 minutes more. Remove thyme sprigs. Transfer the meat mixture to a 9x13 baking dish.
7While the meat cooks, mash the hot potatoes with butter, milk, salt, and pepper until smooth and creamy.
8Spread mashed potatoes evenly over the filling. Sprinkle cheddar across the top.
9Bake for 15–20 minutes until potatoes are light golden and filling bubbles at the edges. Let rest 5 minutes before serving.