Peel potatoes, and slice thinly with mandoline if possible.
Preheat the oven to 375°F (190°C).
Melt butter in a microwave-safe bowl or small saucepan on low heat.
Mix Parmesan, salt, pepper, garlic, and onion into melted butter.
Toss potato slices in the butter mixture until well coated.
Grease a 9-inch pie dish or cast-iron skillet.
Arrange potato slices overlapping in a dish or skillet, and fill gaps.
Drizzle the remaining butter over the potatoes.
Cover the dish with foil, and bake for 30 minutes.
Uncover, and bake for 15-20 minutes until tender and golden edges.
Cool a bit before slicing and serving.