Preheat the oven to 350 degrees and prepare a 9x13in pan with non stick spray.
Melt the butter in a medium to large sauce pan over medium heat.
Add in the flour and cook until the flour is mixed into the butter, about 2 minutes.
Pour in the half and half, stirring regularly, until the mixture is thickened, about 2 minutes.
Remove from heat and add in the salt and pepper, and 2 cups of the shredded cheese.
Layer about 1/3 of the sliced potatoes into the pan. Pour 1/3 of the cheese sauce over the top.
Repeat with another third potatoes, cheese sauce, potatoes and cheese sauce.
Cover with foil and bake for about 40 minutes.
Remove the foil and sprinkle with additional 1/2 cup of cheese and bake for another 20 minutes or so until the sauce is bubbly and the potatoes are soft.