Step 1
Preheat oven to 400 degrees F (200 degrees C). Coat an 8-inch baking dish cooking spray.
Step 2
Mix Parmesan cheese rosemary and garlic together in a bowl.
Step 3
Slice 3 or 4 potatoes using a mandolin on the thinnest setting. Slice remaining potatoes using a slightly thicker setting on the mandolin.
Step 4
Line the bottom of the prepared baking dish with thin potato slices overlapping them to create a layer that is 2 to 3 slices deep. Stand remaining thin slices along the sides of the baking dish so that half an inch sticks over the rim overlapping them to create a layer that is 4 slices deep.
Step 5
Spread 1/3 of the thicker potato slices in the baking dish. Sprinkle 1/3 of the Parmesan cheese mixture on top. Repeat once more. Arrange remaining potato slices in the baking dish. Reserve 1/3 of the Parmesan cheese mixture.
Step 6
Melt butter in a saucepan over medium heat; whisk in flour. Pour in milk; cook stirring occasionally until sauce thickens 5 to 6 minutes. Stir in salt.
Step 7
Shift potato slices in a few places with a knife to create wells for the sauce to flow through. Pour sauce evenly over potato slices in the baking dish. Sprinkle remaining 1/3 of the Parmesan cheese mixture on top. Brush potato edges sticking out of the baking dish with olive oil.
Step 8
Bake in the preheated oven until potatoes are soft and edges are crusted 60 to 75 minutes.