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.