Preparation Preheat oven to 375°F. Brush 13x9x2-inch glass or oval ceramic baking dish with 2 tablespoons oil. Arrange 1/3 of potatoes, slightly overlapping, in dish. Sprinkle with 1/2 teaspoon coarse salt and 1/4 teaspoon pepper. Pour 1/3 cup cream over; sprinkle with 1/4 cup cheese. Repeat layering 1/3 of potatoes, 1/2 teaspoon salt, 1/4 teaspoon pepper, 1/3 cup cream, and 1/4 cup cheese 2 more times. Bake uncovered until potatoes are tender, adding cream by tablespoonfuls if dry, about 45 minutes. Remove from oven; maintain oven temperature. Sprinkle thyme and garlic slices over gratin. Toss mushrooms in medium bowl with 3 tablespoons oil; sprinkle with coarse salt and pepper. Arrange mushroom slices atop gratin around edge of dish. Drizzle with 1/4 cup cream; sprinkle with 1/4 cup cheese. Continue to bake uncovered until mushrooms are tender and potato edges are golden brown, about 20 minutes longer. DO AHEAD: Can be made 1 day ahead. Cool 1 hour in dish; cover and chill. Before serving, cut gratin into 10 pieces. Transfer to rimmed baking sheet. Cover with foil and rewarm in 350°F oven, 10 to 15 minutes.
Preparation Preheat oven to 375°F. Brush 13x9x2-inch glass or oval ceramic baking dish with 2 tablespoons oil. Arrange 1/3 of potatoes, slightly overlapping, in dish. Sprinkle with 1/2 teaspoon coarse salt and 1/4 teaspoon pepper. Pour 1/3 cup cream over; sprinkle with 1/4 cup cheese. Repeat layering 1/3 of potatoes, 1/2 teaspoon salt, 1/4 teaspoon pepper, 1/3 cup cream, and 1/4 cup cheese 2 more times. Bake uncovered until potatoes are tender, adding cream by tablespoonfuls if dry, about 45 minutes. Remove from oven; maintain oven temperature. Sprinkle thyme and garlic slices over gratin. Toss mushrooms in medium bowl with 3 tablespoons oil; sprinkle with coarse salt and pepper. Arrange mushroom slices atop gratin around edge of dish. Drizzle with 1/4 cup cream; sprinkle with 1/4 cup cheese. Continue to bake uncovered until mushrooms are tender and potato edges are golden brown, about 20 minutes longer. DO AHEAD: Can be made 1 day ahead. Cool 1 hour in dish; cover and chill. Before serving, cut gratin into 10 pieces. Transfer to rimmed baking sheet. Cover with foil and rewarm in 350°F oven, 10 to 15 minutes.