Heat the oil in a large saucepan, add the onion, celery and carrots and cook for 3–4 minutes until softened. Increase the heat, stir in the mushrooms and cook for a further 3 minutes, stirring occasionally.
Add the lentils, tomatoes, tomato purée and stock. Bring to the boil, then reduce the heat and simmer, uncovered, for 15 minutes. Season to taste with salt and pepper. Transfer to a 2 litre (3½ pint) ovenproof dish.
Meanwhile, cook the parsnips and potatoes in a large saucepan of lightly salted boiling water for 20 minutes or until tender.
Drain the root vegetables and return to the pan. Mash with the milk and butter, then season to taste with salt and pepper.
Spoon the parsnip mash over the lentil mixture and scatter over the cheese. Bake in a preheated oven, 190°C (375°F), Gas Mark 5, for 20 minutes until golden and bubbling.