Potato, Leek, Gruyère and Oyster Mushroom Gratin

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.