Cook the carrots and swede/sweet potato in boiling lightly salted water for 20 minutes or until tender and then mash with the knob of butter until smooth.
Heat half a tablespoon of the oil in a large non-stick frying pan and sauté the minced beef for 7 or 8 minutes or until the liquid has been evaporated. Remove the beef from the pan and set aside.
Heat the remaining 2 tablespoons of oil in a fairly large casserole and sauté the onion and leek for 3 minutes. Add the red pepper and sauté for 2 minutes, then add the mushrooms and garlic and sauté for 4 minutes. Add the tomatoes and sauté for 3 minutes. Add the tomato puree, Worcestershire sauce, herbs and beef stock and simmer for about 30 minutes. Season to taste.
Meanwhile, boil the potatoes for 15 to 20 minutes, then drain. Return the cooked potatoes to the empty saucepan and mash together with butter, milk salt and pepper until smooth.
Place the mashed carrots and swede in the base of a glass ovenproof dish (approximately 18cm diameter / 7.5 cm deep) or use mini dishes to make individual portions. Arrange the meat on top, then cover with a layer of cooked peas and top with a layer of potato.
Brush the potato with the beaten egg and cook under a preheated grill for 6 to 7 minutes or until the top is browned.