Preheat the oven to 190C/375F/Gas 5.
For the topping, place the potatoes and parsnips or swede into a large pan of water. Bring to the boil and cook for 12-15 minutes, or until tender. Drain well.
Add the butter to the cooked vegetables and mash using a potato masher or ricer. Add the milk, a little at a time, and continue to mash until smooth. Season, to taste, with salt and freshly ground black pepper. Set aside.
For the filling, heat the oil in a large pan over a low to medium heat. Add the onion and fry for 8-10 minutes, or until softened.
Add the garlic, carrot, leek and thyme and continue to fry for a further 4-5 minutes, or until softened.
Add the vegetarian mince to the pan and fry for a further 2-3 minutes, stirring continuously, or until golden-brown.
Add the drained cannellini beans, chopped tomatoes and tomato purée and stir well to combine. Bring the mixture to a simmer and continue to simmer for as further 4-5 minutes, or until the sauce has thickened. Season, to taste, with salt and freshly ground black pepper. Taste and add a little sugar to the mixture if needed.
Spoon the filling mixture into a large ovenproof dish. Spread the mashed potato and parsnip (or swede) mixture over the filling in a smooth, even layer.
Transfer to the oven and cook for 18-20 minutes, or until the topping is golden-brown and the filling is cooked through.
Serve with steamed green vegetables.