Prepare the mash: Peel the potatoes and cut them into even 4cm chunks. Place them in a large pan of cold, salted water and bring to a boil. Cook for 15-18 minutes until a knife slides through the thickest piece with no resistance — the potatoes should feel tender and look slightly fluffy around the edges.

Mash them smooth: Drain the potatoes well and return them to the hot pan for 30 seconds to steam off excess moisture. Add the butter and warm milk, then mash until smooth. The mash should look creamy and glossy, with a rich buttery aroma. Season with salt and pepper, and stir in the egg yolk if using. Set aside.

Sweat the vegetables: While the potatoes cook, heat the oil in a large ovenproof skillet or deep frying pan over medium heat. Add the onion, carrots, and celery. Cook for 6-8 minutes, stirring occasionally, until the onions turn translucent and the carrots soften — you'll notice a sweet, savoury fragrance filling your kitchen. Add the garlic and cook for 1 minute until it smells fragrant.

Brown the beef: Increase the heat to medium-high and add the minced beef. Break it apart with a wooden spoon and let it brown undisturbed for 2-3 minutes before stirring. Continue cooking for 5-6 minutes total until the beef is no longer pink and you can hear a satisfying sizzle. The meat should look deep brown, not grey, with small crispy bits sticking to the pan.

Build the sauce: Stir in the tomato purée and cook for 1 minute — it will darken and smell richer. Sprinkle over the dried thyme, then pour in the beef stock and Worcestershire sauce. Bring to a gentle simmer; the liquid will bubble steadily and the aroma will become deeply savoury. Let it simmer for 5 minutes until the sauce thickens slightly and coats the back of a spoon.

Finish the filling: Stir in the frozen peas and cook for 2 minutes. The peas will turn bright green and the sauce should be thick enough to hold its shape on a spoon. Taste and adjust seasoning with salt and pepper. The filling should look glossy and rich, with the vegetables evenly distributed.

Assemble and bake: Preheat your oven to 200°C (180°C fan) or Gas Mark 6. Spoon the mashed potato over the beef filling, spreading it gently from the edges towards the centre. Use a fork to create peaks and swirls across the surface — these will crisp up beautifully. Place the pie on a baking tray to catch any bubbling juices and bake for 20-25 minutes until the filling is bubbling at the edges and the potato topping is golden brown with darker crunchy peaks. Let it rest for 5 minutes before serving — this allows the sauce to settle and prevents it from running across the plate.