This dish can be served as main course for vegetarians, or as a side dish. Combine with a spring lamb chop or pork tenderloin for a hearty meal.
- Put oven rack in middle position and preheat to 400°F.
- Cook chanterelles or shiitakes with salt and pepper to taste in 1 tablespoon butter in a large nonstick skillet over moderate heat, stirring, until liquid mushrooms give off is evaporated and mushrooms are tender, about 8 minutes, then transfer to a bowl.
- Cook cremini in remaining 1 1/2 tablespoons butter in skillet, stirring, until liquid is evaporated and mushrooms are tender, about 8 minutes, then transfer to bowl with wild mushrooms. Toss mushrooms with 1 teaspoon garlic.
- Peel potatoes and cut crosswise into 1/8-inch-thick slices using a mandolin or electric slicer for uniformity. Store in cold salted water until ready to use, then pat dry.
- Bring potatoes, cream, milk, salt, white pepper, nutmeg, and remaining 1/2 teaspoon garlic to a boil in a 4- to 6-quart heavy pot, stirring once or twice, then remove from heat.
- Transfer half of potatoes to buttered 15- by 10- by 2-inch oval gratin dish or other 3-qt shallow baking dish with a slotted spoon, spreading evenly. Spread mushrooms evenly over potatoes, then top with remaining potatoes. Pour cooking liquid over potatoes and sprinkle with cheese.
- Bake gratin until top is golden brown and potatoes are tender, 45 to 55 minutes. Let stand 10 minutes before serving.