Preheat your oven to 375°F (180°C). Butter a 9" pie plate and set aside.
Slice potatoes thinly. Place a thin layer of potatoes in the pie plate. Add a layer of garlic, Parmesan and butter. Repeat until the potatoes are all used up. Reserve a small amount of butter and Parmesan cheese and set aside.
In medium saucepan heat milk (but do not bring to a boil) and gently pour over the potato pie. Top with breadcrumbs and remaining cheese and butter. Bake for 1 hour, until the potatoes are tender and top has turned golden brown.