4 tablespoons (1/2 stick) butter
1 pound oyster mushrooms, halved if large
1 tablespoon minced garlic
4 cups thinly sliced leeks (white and pale green parts only; about 4 large)
1 tablespoon minced fresh thyme
1 3/4 cups canned low-salt chicken broth
1 3/4 cups whipping cream
1/4 cup dry white wine
1 teaspoon salt
1/2 teaspoon ground black pepper
3 3/4 pounds russet potatoes, peeled, thinly sliced into rounds (about 8 cups)
2 1/2 cups grated Gruyère cheese (about 10 ounces)
Melt 2 tablespoons butter in heavy large skillet over medium-high heat. Add mushrooms and sauté until almost tender, about 5 minutes. Add garlic and sauté until mushrooms are tender and golden, about 3 minutes longer. Transfer mushroom mixture to bowl. Melt remaining 2 tablespoons butter in same skillet over medium-high heat. Add leeks and thyme and sauté until leeks are tender and beginning to brown, about 8 minutes. Add leek mixture to bowl with mushrooms. (Can be made 1 day ahead. Cover and refrigerate.)
Preheat oven to 400°F. Butter 13 x 9 x 2-inch baking dish. Whisk broth, cream, wine, 1 teaspoon salt and 1/2 teaspoon pepper in large bowl to blend. Layer 1/3 of potatoes on bottom of prepared dish. Top with half of mushroom-leek mixture, then 3/4 cup cheese. Top with half of remaining potatoes. Pour half of cream mixture over. Top with remaining mushroom-leek mixture and 3/4 cup cheese. Cover with remaining potatoes. Pour remaining cream mixture over; sprinkle with remaining cheese.
Bake gratin uncovered until potatoes are tender and sauce bubbles thickly, about 1 hour 20 minutes. Let gratin stand 30 minutes before serving.