Place the chopped potatoes in a large saucepan and cover them with cold water. Bring to a boil, then reduce the heat and simmer for approximately 15–20 minutes, or until the potatoes are completely tender when pierced with a fork. Drain thoroughly and return them to the warm pan for a minute to release excess moisture.

Add the butter and warm milk to the drained potatoes. Mash until smooth and creamy, adding the milk gradually so the topping doesn’t become too loose. Season with black pepper and a little salt if needed. If using cheese, reserve most of it for the top rather than mixing all of it into the potatoes.

Heat the vegetable oil in a large frying pan over medium heat. Add the chopped onion and carrot, cooking for about 4–5 minutes until they begin to soften. Stir in the garlic, then add the ground beef and cook until browned, breaking it apart with a wooden spoon. Drain excess fat if necessary.

Stir in the tomato paste, chopped tomatoes, baked beans, Worcestershire sauce, smoked paprika, mixed herbs, and a little black pepper. Add some beef stock if the mixture seems too thick, then simmer for 8–10 minutes until the vegetables soften and the sauce becomes rich. Taste the filling and adjust the seasoning before assembling the pie.

Preheat the oven to 200°C (400°F). Transfer the beef-and-bean mixture to an ovenproof baking dish and spread it into an even layer. Spoon the mashed potatoes over the top, spreading them gently to cover the filling completely. Use a fork to create ridges across the mash, then sprinkle with grated cheddar if desired.

Place the dish in the preheated oven and bake for approximately 20–25 minutes, until the filling bubbles around the edges and the potato topping turns lightly golden. If you prefer a more browned surface, place it under the grill briefly, watching carefully to prevent burning. Let the pie stand for 5–10 minutes before serving so the filling settles.