Preheat the oven to 200°C (400°F).

Heat the olive oil in a large pan over medium heat. Add the onion, garlic, carrot, and celery. Sauté for 5–7 minutes until softened and fragrant.

Turn the heat up to high and add the ground beef. Break it up with a wooden spoon and cook until browned with no pink remaining. Drain excess fat if the pan is very greasy.

Stir in the tomato paste and Worcestershire sauce. Mix well so the paste coats the meat and starts to caramelize.

Pour in the beef stock, add the thyme, and season with salt and pepper. Reduce heat and simmer uncovered for about 20 minutes, stirring occasionally.

While the meat simmers, place the potatoes in a large pot of salted water. Boil until tender, about 15–20 minutes. Drain well and return to the pot.

Add the warm milk and butter to the potatoes and mash until smooth. Season with salt and pepper.

Spoon the beef mixture into a large ovenproof dish and spread evenly.

Top with the mashed potatoes, smooth with a spatula, and sprinkle over the grated cheddar.

Bake in the preheated oven for 25–30 minutes, until the potato topping is golden and the filling bubbles at the edges.

Remove from the oven and let rest for 5 minutes. Garnish with chopped parsley if desired, then serve.