Melt butter in a medium saucepan on medium low heat. Stir in flour. Continue stirring; the mixture will clump up a bit. Continue cooking for one minute, stirring often (this helps cook the "floury" taste out of it). Stir the milk, salt and pepper into butter mixture. Continue to cook on medium heat until mixture thickens considerably. Add sharp cheddar cheese; stir until cheese has fully melted, and sauce is quite thick.
Peel, then slice potatoes into 1/8" round slices. If you have a mandoline, use that to get very thin slices. If using a knife to slice potatoes, slice them as thin as possible (no more than 1/4" thin). If the potatoes slices are too thick, it will take much longer to cook them until tender! The thinner the slices are, the better!
Add potatoes to the cheese sauce in pan. Stir well, to completely cover potatoes. Spray a 2 quart sized baking dish with non-stick spray (bottom and sides). Add potatoes to the dish, and evenly spread to disperse. Set aside.
Make the buttery crumb topping by mixing together melted butter and soft breadcrumbs. Sprinkle the buttered bread crumbs over the entire surface of the au gratin potatoes.
Bake potatoes in a preheated 400 degree oven for 60 minutes (covered with foil). Remove foil and continue baking for an additional 15 minutes, or until surface of potatoes is golden brown and cheese sauce is bubbly around the edges of dish. Remove from oven, season with additional salt and pepper, if desired. Serve, and enjoy!
Au Gratin Potatoes https://www.thegratefulgirlcooks.com/au-gratin-potatoes/