Bring a pot of water to a boil and drop the potatoes into it. Cook for five minutes. Drain and cool.
Crush the garlic cloves, and use them to wipe the inside of a 12-by-8-inch glass baking dish. Discard what's left of the garlic.
Layer the potato slices all the way across the bottom of the dish, sprinkling the cheeses and a little salt and white pepper between the layers.
Beat the egg yolks and mix them into the whipping cream. Pour the mixture over the potatoes. It should come up about two-third of the way to the top. Cover with aluminum foil, and bake in the oven for an hour.
Remove the foil. Combine the bread crumbs and the Parmesan cheese, and sprinkle in a thin layer over the top of the potatoes. Return, uncovered, to the oven. Continue baking until the crust browns. (If you have a convection oven, set it to convect.)
Remove from the oven and allow to rest and cool for at least fifteen minutes before serving.