Preheat your oven to 375°F (190°C).
In a large skillet, brown the ground lamb or beef over medium heat until cooked through. Drain any excess fat.
Add the diced onion, carrots, and minced garlic to the skillet. Cook until the vegetables are softened, about 5 minutes.
Stir in the tomato paste, beef broth, Worcestershire sauce, dried thyme, frozen peas, salt, and pepper. Let the mixture simmer for another 5-10 minutes, allowing the flavors to meld together.
While the filling is simmering, prepare the mashed potatoes. Boil the peeled and cubed potatoes in a pot of salted water until tender, about 15-20 minutes. Drain the potatoes and mash them with butter, milk, salt, and pepper until smooth and creamy.
Transfer the filling to a baking dish and spread the mashed potatoes evenly over the top. For an extra indulgent touch, sprinkle shredded cheddar cheese over the mashed potatoes.
Place the dish in the preheated oven and bake for 25-30 minutes, or until the mashed potatoes are golden brown and the filling is bubbling around the edges.
Remove from the oven and let it cool for a few minutes before serving. Enjoy your delicious Irish Shepherd's Pie!