Prepare the potatoes: Place the sliced potatoes in a large bowl of cold salted water and leave them to soak for 10 minutes. This draws out excess starch, helping them achieve a better texture. Drain them well and pat them thoroughly dry with a clean tea towel. You want them as dry as possible before they go into the dish.

Brown the beef: Heat a large, heavy-based frying pan or Dutch oven over a high heat. Add a splash of olive oil, then add the beef mince. Let it sit undisturbed for 2-3 minutes — you should hear a vigorous sizzle and see the underside turn a deep mahogany brown. Break the mince apart with a wooden spoon and continue cooking until all the pieces are browned and the juices have mostly evaporated. The sound will shift from a wet, steaming hiss to a drier, sharper crackle. Remove the beef with a slotted spoon and set it aside in a bowl.

Sweat the vegetables: Reduce the heat to medium. Add the diced onion, carrot, and celery to the same pan. There should be enough fat left from the beef to coat them. Stir occasionally for 8-10 minutes, until the onion turns translucent and the carrots soften. You'll notice the raw, sharp smell of the onion mellow into a sweet, savoury fragrance. Add the minced garlic and cook for one more minute, until it smells fragrant.

Build the sauce: Stir in the tomato purée and cook for 2 minutes, stirring constantly. It will darken in colour and smell richer. Return the browned beef to the pan, along with any juices that have collected in the bowl. Pour in the beef stock and Worcestershire sauce, then add the dried thyme and smoked paprika. Stir everything together and bring it to a gentle simmer. You should see small bubbles lazily breaking the surface. Season with salt and pepper, then let it cook uncovered for 10-15 minutes, until the sauce has thickened and reduced slightly. It should look glossy and coat the back of a spoon.

Layer the casserole: Preheat your oven to 190°C (170°C fan). Grease a 9x13 inch baking dish with a little butter or oil. Spread one-third of the meat sauce evenly across the bottom. Arrange a single, slightly overlapping layer of potato slices over the sauce. Scatter over a handful of the mixed grated cheeses. Repeat these layers — meat, potatoes, cheese — twice more, finishing with a final layer of potatoes topped with the remaining cheese. The top should look generously covered in ragged patches of yellow and white.

Bake to perfection: Cover the dish tightly with aluminium foil and bake for 40 minutes. After 40 minutes, remove the foil. The casserole should be bubbling visibly at the edges. Increase the oven temperature to 200°C (180°C fan) and bake for a further 25-30 minutes, uncovered. Watch the top carefully in the final minutes. You are looking for the cheese to turn a deep, blistered gold and the edges of the exposed potatoes to crisp and brown. The smell in your kitchen will be intensely savoury and slightly sweet from the caramelising potatoes.

Rest and serve: Remove the dish from the oven and let it rest on a wire rack for at least 10 minutes. This crucial step allows the filling to settle and firm up slightly, preventing it from flooding the plate when you serve. Garnish with a scattering of fresh parsley and serve directly from the dish.