How to Make It
Preheat the oven to 400°. Bring the stock to a boil in a medium saucepan. Add the shallots, cover partially and cook over low heat until tender, about 5 minutes. Strain the stock and spread the shallots in a large oval gratin dish. Keep the stock warm.
Arrange a quarter of the potatoes in a slightly overlapping layer over the shallots and season with salt and pepper. Spread another quarter of the potato slices on top, sprinkle with half each of the Parmesan and chives and season with salt and pepper. Make 2 more layers with the remaining potatoes, seasoning each layer. Add enough stock so that the top layer of potatoes is just above the liquid. Sprinkle with the remaining Parmesan and chives and the Gruyère. Bake for about 1 1/4 hours, or until the potatoes are tender and the top is browned. Let rest for 10 minutes, then serve.