1/2 lb fresh wild or exotic mushrooms such as chanterelles or shiitakes (discard shiitake stems),trimmed and coarsely chopped
2 1/2 tablespoons real butter
3/4 lb fresh cremini mushrooms, trimmed and sliced 1/4 inch thick
1 1/2 teaspoons minced garlic
3 lb russet (baking) potatoes
1 1/2 cups heavy cream
1 1/2 cups whole milk
1 1/2 teaspoons salt
1/2 teaspoon white pepper
1/4 teaspoon freshly grated nutmeg
2 oz finely grated Gruyère (1 cup)
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.
For a more elegant presentation, cut out rounds or diamonds from the gratin with a 4-inch cookie cutter.