Place the celery, carrots, parsnip, turnip and peas into a large saucepan and fill with 5cm water. Bring to a boil, cover, and simmer for 15 minutes or until vegetables are tender.
Meanwhile, cook the lamb, onion and garlic in a large frying pan over medium heat until the lamb is browned. Drain off any excess fat. Stir in the steamed vegetables and tomato puree. Season with salt, pepper, thyme and sage. Transfer everything to a greased 18cm x 28cm baking dish.
Mix enough milk into the mashed potatoes to make the mixture spreadable. Spread over the top of the lamb and sprinkle with parmesan.
Bake for 25 minutes or until the top is browned and the casserole is heated through.