Melt the butter in a medium saucepan over medium heat. Stir in the flour and cook until bubbly, about 1 minute. Whisk in the milk, salt, pepper, and parsley. Cook, stirring constantly, until the mixture thickens and boils. Remove from heat and stir in 1 cup of the Parmesan cheese.
Lightly grease a 2-quart baking dish. Layer the potatoes and onion in the dish. Pour the cheese sauce over the potatoes and onion. Sprinkle with the remaining Parmesan cheese.
Bake for 30 minutes, or until potatoes are tender and top is golden brown.
Interesting Facts
Parmesan cheese is an Italian cheese made from cow's milk.
Au gratin dishes are usually baked with a cheese or bread crumb topping.
The French term "au gratin" literally means "with gratings", referring to the grated cheese used to top the dish.