Preheat the oven to 190C/375F/Gas 5.
Heat the oil in a large pan. Add the onion and carrot and cook over a medium heat for five minutes until soft.
Add the minced beef and cook for three minutes to brown.
Add the tomatoes, purée, beef stock, bay leaf and thyme.
Cover and simmer for 30 minutes. Season.
Meanwhile, to make the topping, boil the potatoes and parsnips in water until soft. Drain and mash with the butter and milk. Stir in the horseradish and season with salt and pepper.
Spoon the meat into an ovenproof dish. Top with the mash and bake for 30 minutes until golden brown.