Place peeled and cubed Yukon Gold potatoes in a large pot. Cover with salted water and bring to a gentle boil. Cook until tender when pierced with a fork, about fifteen minutes.

Drain the cooked potatoes and return them to the pot. Add butter, warm milk, grated Parmesan, salt, and pepper. Mash until smooth and creamy, then set aside while preparing the filling.

Heat olive oil in a large skillet over medium heat. Add chopped onion and diced carrots. Cook gently for five minutes until softened, then stir in minced garlic and cook for another minute.

Add ground lamb to the skillet with the vegetables. Cook while breaking it apart with a spoon until browned and fully cooked. Drain any excess fat to keep the filling rich but not greasy.

Stir tomato paste into the lamb mixture and cook for one minute. Pour in beef broth, then add peas, rosemary, thyme, salt, and pepper. Simmer gently for five minutes until slightly thickened.

Preheat the oven to 400°F. Transfer the lamb filling into a greased 9x13-inch baking dish. Spread the mashed potatoes evenly over the top, creating gentle peaks with a fork for a golden finish.

Place the assembled Shepherd’s Pie in the preheated oven. Bake for about twenty-five minutes until the top turns golden and the filling bubbles around the edges. Allow to rest briefly before serving.