Start by peeling and chopping the starchy potatoes into chunks. Place them into a large pot, cover with cold water, and season with salt. Bring the pot to a boil over medium-high heat. Once boiling, reduce to medium and let them cook until tender, about 15-20 minutes.

While the potatoes are boiling, heat the olive oil in a large skillet over medium heat. Add the finely chopped onion and diced carrot. Sauté for about 5-7 minutes until the vegetables soften. Next, add the ground beef or lamb, breaking it apart with a spoon. Cook until browned, about 10 minutes.

Once the meat is browned, sprinkle in the flour, stirring constantly to coat the meat and prevent lumps. Cook for a minute, allowing the flour to absorb the juices. Gradually whisk in the broth and Worcestershire sauce, stirring until it thickens. Then, mix in the frozen peas, smoked paprika, garlic powder, thyme, and parsley. Season generously with salt and black pepper. Let it simmer for a few minutes.

Once the potatoes are tender, drain them and return them to the pot. Add the butter, heavy cream, sour cream (or cream cheese), and egg yolk. Mash them until smooth, adjusting the cream as necessary for your desired consistency.

Preheat your oven to 400°F (200°C). In a rectangular baking dish, spoon the meat filling, spreading it evenly. Top it with the mashed potatoes, smoothing it out with a spatula. Creating small peaks with a fork will yield a lovely crispy topping.

Place the dish in the preheated oven and bake for about 25-30 minutes, or until the top is golden brown. Let it cool for a few minutes before serving.