Saute the Vegetables - Set a large 12-inch oven-safe skillet or cast iron pan over medium-high heat. Add olive oil. Once hot, add the onions, carrots, and celery. Saute for 3 minutes. Add the garlic and saute until fragrant, 30 seconds. Add rosemary and thyme, and saute for 30 seconds. Add the tomato paste and saute for 1 minute.

Cook the Meat - Add the ground lamb and beef to the pan. Saute until lightly browned, about 5 minutes.

Thicken the Filling - Stir in salt, pepper, and flour. Add beef stock and Worcestershire sauce. Bring the liquid to a simmer and cook until thickened, 4 to 5 minutes.

Add the Peas - Stir in the peas and cook until warmed, about 1 minute. Taste the filling and season with salt and pepper as needed.

Preheat the Oven – Set the oven rack to the middle position and the temperature to 400ºF (204ºC). If your pan is not oven-safe, the filling can be transferred to a 9 by 13-inch baking dish.

Prepare the Potatoes - In a large pot, add water and 1 teaspoon of salt, bring to a boil. Peel the potatoes and cut them into 1-inch pieces. Add them to a colander and rinse under cool water until the starchy water is transparent. Drain well.

Cook the Potatoes - Add the potatoes to the boiling water and cook until fork-tender, about 15 minutes. Drain and rinse them with hot water to remove any residual starches, 30 seconds.

Mash the Potatoes - Set a food mill or fine mesh strainer over the pot used to cook the potatoes. Press and pass them through into the pot. Alternatively, use a potato masher. Add butter and gently fold it in. Microwave the milk for 30 to 45 seconds until warm, about 120ºF (49ºC). Add ½ teaspoon of salt to the milk and whisk to dissolve. Gradually fold the milk into potatoes in three additions until the milk is absorbed. Add egg yolk and stir until combined.

Add Potatoes to the Pan - Evenly spread the mashed potatoes over the meat filling. Make sure to cover the edges of the dish to keep the filling from rising up the sides.

Bake and Broil - Cook in the middle of the oven for 20 minutes to warm the potatoes and dry the surface. Turn the oven to the broil setting and cook until the surface is golden brown, about 2 to 3 minutes.

Serve - Allow the dish to rest for 10 minutes before serving. Garnish with black pepper and chopped parsley.