Step 1Heat oven to 375 degrees and put a jellyroll pan in the bottom of the oven to catch any drips. Slice the potatoes crosswise as thinly as possible (a Japanese slicer makes this very easy).
Step 2Put the potatoes in a 3-quart saucepan and add the milk, cream, garlic, bay leaf and salt. Cover and bring to a gentle simmer. When the liquid starts to bubble around the edges, remove the lid and cook until the potatoes are firm but tender, about 20 minutes in all.
Step 3Rub the inside of a large gratin dish with a generous amount of butter. Using a slotted spoon, transfer about half of the potatoes to the dish and arrange in an even layer.
Step 4Stir together the caramelized onions and the prosciutto and distribute this evenly across the potatoes (it will be just enough to form a very thin layer).
Step 5Pour the remaining potatoes and cooking liquid into the gratin dish, arranging the potatoes in an even layer. There should be enough liquid to almost cover the potatoes. Scatter the cheese over top and bake until the top is bubbly and evenly browned, about 1 hour.