Preheat the oven to 375 degrees F and put a rack in the middle of the oven.

Grease a 13 x 9 inch baking dish.

Use a mandolin (if possible) or a sharp knife to slice the potatoes into 1/8-inch thick rounds, and transfer them into a bowl of cold water.

Saute the onion in the oil and butter for 5 minutes or until tender, then stir in the garlic and cook for another minute.

Stir in the milk and cream, and bring the mixture to a simmer.

Drain the potatoes and use paper towels to dry them. Layer half of them in the baking dish and sprinkle half the salt and pepper on top. Now sprinkle half the cheese over that.

Repeat with the rest of the potatoes, salt, black pepper and cheese.

Now you can pour the cream mixture over the top, pressing the potato slices down to submerge most of them.

Cover the dish with aluminum foil and bake for an hour on the middle rack.

Remove the foil and give them another half an hour, or cook them until the top is golden brown and the potatoes have soaked up most of the liquid.

Keep an eye on the potatoes - if they are browning too quickly, you can loosely cover the dish with aluminum foil and then resume baking.

Once the potatoes are fork-tender, the dish is ready to serve.

We suggest letting it sit on the countertop for 10 minutes though, since it will be piping hot from the oven.