Preheat the oven to 190°C.
Boil potatoes and parsnips in a large pan for 12 to 15 minutes and drain.
Mash the vegetables with butter and milk until smooth, then season.
Fry the onion in oil for 8 to 10 minutes until softened.
Add garlic, carrot, leek, and thyme and fry for 5 minutes.
Stir in the vegetarian mince and cook for 3 minutes until browned.
Add beans, tomatoes, and tomato purée, simmering for 5 minutes until thickened.
Spoon filling into an ovenproof dish and top with the mash in an even layer.
Bake for 18 to 20 minutes until the top is golden.
Serve the pie alongside steamed green vegetables.