To make the root vegetable topping
Peel and dice the potatoes and root vegetables into 2cm cubes. Place in a pan of salted boiling water, return to the boil and simmer for around 15 minutes, until tender. Drain and mash the root vegetables along with the butter and milk. Season to taste.
To make the meat base
Brown the mince in a large saucepan for around 5 minutes. While the mince is browning, peel and finely slice the carrot using a food processor. Do the same with the onion, but not quite as fine as the carrot. (If you do not have a food processor, grate the carrot and finely chop the onion).
Drain the fat off and put mince to one side. Put the onion and carrot into the pan which had the mince in. Cook for 3-4 minutes until soft. Return the mince to the pan along with the tomatoes, stock, thyme, tomato puree, garlic and peas. Add salt and pepper to taste. Simmer for 10-15 minutes.
To assemble the pie
Build the pie by spooning the mince evenly into the bottom of an ovenproof dish (or individual dishes if you prefer). Top with an even layer of mashed vegetables and use a fork to make furrows all over the top. Dot the top with butter to help the it crisp and sprinkle with grated cheese if you like.
Bake for around 10 minutes in a hot oven until the top is crispy and the sauce bubbles around the edges of the dish. (Use a hot grill if time is limited).
Tenderstem broccoli or any other green vegetable you prefer.
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