1. Heat 2 tablespoons oil in a large Dutch oven over medium-high heat. Season lamb generously with salt and pepper. Cook a third of the lamb, until golden brown, 4 to 5 minutes per side. Transfer to a bowl. Stir in 1/4 cup stock, scraping up any browned bits on the bottom. Pour liquid over browned lamb. Repeat with oil, lamb, and stock. After the last batch, do not pour out stock.

2. Add onions, garlic, and rosemary to pot, and cook, stirring occasionally, for 5 minutes. Return browned lamb and juices from bowl to pot. Add remaining 3 1/4 cups stock. Bring to a boil, reduce heat, and cover. Simmer until meat is tender, about 1 hour.

3. Preheat oven to 400 degrees. Using a mandoline or handheld slicer, slice potatoes thinly. Rinse, then pat dry. Toss with remaining 2 tablespoons oil.

4. Cover bottom of a 12-inch gratin dish with half the potato slices: starting at outer edge, overlap each potato by half, working in concentric circles toward center. (There should be 4 circles.) Spoon lamb and broth over top, then repeat arrangement with remaining potato slices on top of lamb. Sprinkle with rosemary, and season with salt and pepper. Bake until top is gold, edges are crisp, and juices are bubbling, about 1 hour. Let cool slightly before serving.