We stuck with tradition and made our shepherd's pie with lamb, but you could easily swap in ground beef. The saucy filling is packed with tender vegetables and the creamy topping is inspired by the Irish potato dish, colcannon, and is filled with cabbage, leeks and cheese.
For the topping: Put the potatoes in a large saucepan and cover with cold water. Season with 2 teaspoons salt. Bring to a boil and cook until tender, about 20 minutes. Drain and reserve the saucepan.
Meanwhile, make the filling: Heat the olive oil in a large nonstick skillet over medium heat. Add the carrots, onion, celery, garlic, thyme and 2 teaspoons salt. Cook, stirring occasionally, until the vegetables are soft and tender, about 15 minutes.
Stir in the tomato paste and cook until it turns brick red, about 8 minutes. Add the lamb, 1 1/2 teaspoons salt and a few grinds of black pepper. Cook, breaking up with a wooden spoon, until the meat is no longer pink, about 7 minutes.
Stir in the peas. Stir in the flour until incorporated, about 1 minute. Add the broth and Worcestershire and cook until thickened, 3 to 5 minutes.
To finish the topping, melt the butter in the large saucepan over medium heat. Add the cabbage and leeks and cook until tender, about 10 minutes. Add the garlic and cook until fragrant, 1 minute. Add the heavy cream, 1 tablespoon salt, and a few grinds of black pepper, and cook until warm, about 1 minute. Return the potatoes to the pan with the cabbage and add the cheese. Mash with a potato masher or wooden spoon. Remove from the heat and stir in the egg yolks.
Transfer the filling to a 9-by-13-inch baking dish. Add the topping, swirling to create texture. Make sure that the sides are sufficiently covered so the filling doesn't leak through. Bake until the filling is bubbly and the top is lightly golden, about 35 minutes. Let rest 15 minutes before serving.