Begin by preheating your oven to 400°F (200°C). This ensures that your shepherd's pie will bake evenly and develop a beautiful golden crust.
In a large skillet, heat the olive oil over medium heat. Add the ground lamb and cook until browned, breaking it apart with a spatula as it cooks. This should take about 5-7 minutes.
Once the lamb is cooked, add the diced onions and carrots to the skillet. Sauté for an additional 5 minutes until the vegetables are softened. Stir in the minced garlic and cook for another minute until fragrant.
Stir in the Worcestershire sauce, tomato paste, dried rosemary, salt, ground thyme, and black pepper. Mix well to combine all the flavors. Pour in the chicken stock and bring the mixture to a simmer. Allow it to cook for about 10 minutes until slightly thickened.
While the lamb mixture is simmering, place the peeled and chopped potatoes in a pot of salted water. Bring to a boil and cook until the potatoes are fork-tender, about 15-20 minutes.
Drain the boiled potatoes and return them to the pot. Add the egg yolk, heavy whipping cream, butter, and half of the grated Parmesan cheese. Mash until smooth and creamy, adjusting the consistency with additional cream if necessary.
In a casserole dish, spread the lamb mixture evenly across the bottom. Top it with the creamy mashed potatoes, using a spatula to smooth it out. Sprinkle the remaining Parmesan cheese on top for an extra cheesy finish.
Place the shepherd's pie in the preheated oven and bake for about 20-25 minutes or until the top is golden brown and bubbly. You may want to broil it for a couple of minutes at the end for an added crispy texture.
