We love to serve these Swiss potato-and-onion squares with a side of applesauce.
Preheat oven to 375 degrees, with rack in lower third. Generously brush a 17-by-12-inch rimmed baking sheet with oil.
Place onions in a large bowl. Peel potatoes, and grate on the large holes of a box grater, adding them to bowl and stirring into onions as you work to prevent discoloration. Squeeze handfuls of the mixture to release excess liquid, and transfer mixture to another bowl.
Add salt, pepper, cheese, and oil to potato mixture, and toss well to combine. Sprinkle mixture over prepared baking sheet, and press down lightly with your hands to form an even layer.
Bake until golden, about one hour. Remove from oven, and cut into squares. Serve immediately with applesauce.