Prepare the Mashed Potato Topping: Boil the cubed Maris Piper potatoes in salted water until they are fork-tender. Drain the potatoes well and let them dry out briefly in the hot pan to evaporate any excess moisture. Pass them through a potato ricer or mash them until smooth. Stir in the butter, warm milk, and cheese until creamy, then beat in the egg yolk to give the topping structure. Season generously with salt and pepper and set aside.
Brown the Minced Beef: Place your heavy-based frying pan over high heat and add the olive oil. Add the minced beef in batches, allowing it to sear and trigger the Maillard reaction rather than steaming in its own juices. Once the meat is heavily browned, tip it into a sieve to drain the excess fat, which prevents the final gravy from becoming greasy.
Build the Aromatics: In the same pan, add a touch more oil if needed, and fry the diced onions, carrots, celery, garlic, and thyme for about 5 to 10 minutes until softened and lightly golden. Stir in the tomato purée and cook for another 2 to 4 minutes to slightly caramelize the sugars.
Simmer the Thick Glossy Gravy: Return the drained minced beef to the pan. Pour in the full bottle of Guinness and the Worcestershire sauce. Boil the mixture until the dark stout reduces by half, then stir in the beef stock. Reduce the heat and gently simmer for 20 to 30 minutes until you achieve a thick glossy gravy. Remove from the heat and let the filling cool slightly.
Assemble the Dish: Preheat your oven to 180°C (350°F) or up to 200°C (400°F) for an extra crisp top. Spoon the cooled meat filling into your baking dish and press it down slightly. Spread the mashed potatoes over the meat, working from the edges inward to seal the filling, or use a piping bag for neat ridges. Rough up the surface with a fork to create peaks that will catch the heat, and sprinkle the extra cheese on top.
Bake to Perfection: Bake for 25 to 30 minutes until the dish is piping hot, bubbling around the edges, and features a beautifully caramelized crust. Let the pie rest for 10 minutes before serving to ensure it holds its shape.