For the Bechamel Sauce

In a medium saucepan heat the milk until simmering.

In a separate medium sauté pan melt the butter and slowly incorporate the flour, whisking constantly over low heat to make a blonde roux. Slowly incorporate 1 cup of the heated milk to the roux, whisking constantly. Cook over low heat for 10 minutes, until mixture becomes paste-like in consistency. Slowly incorporate the remaining milk and whisk until smooth.

For the Potatoes

Preheat the broiler to the low setting.

Coarsely chop the boiled potatoes. Set a large sauté pan over medium heat and add the potatoes, Béchamel sauce and cheddar cheese and simmer until all of the cheese is melted. Stir until the ingredients are incorporated.  Season the potatoes with salt and pepper.

Transfer the potato mixture to a 13x9x2-inch oven-safe baking dish. Smooth out the top of the potatoes to create an even layer. Mix the breadcrumbs and Parmesan cheese together in a small bowl and sprinkle the mixture over the potatoes. Drizzle the clarified butter over the breadcrumbs and broil the dish for 8 to 10 minutes until a golden brown crust is formed. 

Serve immediately.