2) In a large frying pan, heat 15g of the butter over a medium heat. Add the onion and saute, stirring frequently, until golden, about 10 to 12 minutes. Add the garlic and thyme and cook for 1 minute more. Add the meat, break it up with a wooden spoon, and cook until the meat loses its red colour, about 5 minutes.
3) Add the 1 tsp salt, 1/4 tsp pepper and tomato puree and cook for 1 minute more. Add the chopped tomatoes and bay leaf and bring to a simmer. Cover and cook for 20 minutes. Remove the bay leaf and spoon off any excess fat if needed. Stir in the parsley and add salt and pepper to taste.
4) Heat the remaining 15g butter in a frying pan over a medium-high heat and saute the mushrooms until golden, about 5 minutes. Season with salt and pepper. Set aside.
5) Preheat the oven to 180C/Gas 4. Spread the meat mixture over the bottom of the casserole, top with the mushrooms, and then the carrots and turnips. Beat the egg into the potatoes and spread them completely over the vegetables to finish the pie. Bake for 30 to 40 minutes, until heated through.
6) If desired, sprinkle the cheese on top and grill the pie under a preheated grill. Serve immediately.
For the glazed carrots and turnips:
1) Put the vegetables in a frying pan just large enough to hold them in a single layer. Add enough water so that it comes halfway up their sides, and the butter and sugar. Bring to the boil over a high heat, then adjust the heat to maintain a simmer.
2) Cover the vegetables with a round of greaseproof paper just large enough to fit the inside diameter of the pan, or with a lid set ajar. Simmer the vegetables until tender, about 8 to 10 minutes. Remove the cover and raise the heat to high.
3) Toss the vegetables frequently in the pan, as the liquid evaporates to a shiny smooth glaze. Season with salt and pepper to taste and serve.
For the potato mash:
1) In a large saucepan, combine the potatoes, 1 teaspoon of the salt, and cold water to cover. Bring to the boil over a high heat. Lower the heat to maintain a simmer and cook until fork tender, about 10 minutes. Drain the potatoes and return to the pan. Shake the pan over a medium heat for about a minute to dry the potatoes. Transfer the potatoes to a food mill, ricer, or bowl.
2) Put the milk and butter in the saucepan and heat over a medium-high heat until the milk is hot and the butter melts. Remove the pan from the heat. Mash the potatoes through the food mill, ricer or by hand into the pan. Stir to combine with the milk and butter. Season with salt and pepper to taste, and with nutmeg if desired.