1 garlic clove, halved
Olive oil for brushing plus
4 tablespoons, divided
2 cups chopped onions
Coarse kosher salt
2 1/4 pounds russet potatoes, peeled, very thinly sliced
8 tablespoons (packed) grated Pecorino Romano cheese, divided
3 tablespoons drained capers
2 cups low-salt chicken broth
Preheat oven to 350°F. Rub 13x9x2-inch glass baking dish with cut side of garlic clove. Brush dish with olive oil. Heat 2 tablespoons oil in heavy large skillet over medium heat. Add onions, sprinkle with coarse salt, and sauté until soft and beginning to brown, stirring frequently, about 13 minutes.
Arrange 1/3 of potatoes in even layer in prepared dish. Sprinkle with coarse salt and pepper. Scatter half of onions over. Sprinkle with 2 tablespoons Pecorino Romano and 1 tablespoon capers. Repeat layering with half of remaining potatoes, coarse salt and pepper, remaining onions, 2 tablespoons Pecorino Romano, and 1 tablespoon capers. Drizzle with 1 tablespoon olive oil.
Arrange remaining potato slices over. Sprinkle with coarse salt and pepper and remaining 1 tablespoon capers. Drizzle with remaining 1 tablespoon olive oil. Pour chicken broth over. Press down firmly on potatoes to compact gratin.
Cover gratin tightly with foil and bake until potatoes are tender, about 1 hour 20 minutes. Uncover and sprinkle with remaining 4 tablespoons Pecorino Romano. Bake gratin uncovered until cheese is lightly browned, about 15 minutes. Let gratin stand 10 minutes at room temperature before serving.