1) Preheat oven to 400°F (200°C), Gas Mark 6.
2) Grease a pie dish and keep aside.
3) Cut the potatoes into 1/4 inch (0.5 cm) thick slices.
4) In a pan, sautÃ© the mushrooms in hot butter until tender.
5) In the pie dish, place layers of potatoes, peas, mushrooms and sliced eggs, seasoning with salt and pepper to taste.
6) Pour in milk.
7) Sprinkle grated cheese on top.
8) Place inside oven to bake for 20-30 minutes.
9) Serve the pie piping hot, with tomato sauce or brown sauce on side, if desired.