Preheat your oven to 350°F (175°C) and grease a medium-sized casserole dish with butter.

Melt 4 tablespoons of butter in a saucepan over medium heat, then add 4 tablespoons of all-purpose flour to create a roux and whisk for about 2 minutes.

Slowly add 2 cups of milk while stirring, then season with salt and let simmer on low heat until thickened.

Remove from heat and stir in 1 cup of shredded sharp cheddar cheese until melted.

Layer one-third of the sliced potatoes in the greased casserole dish, season with salt and pepper, then pour one-third of the cheese sauce over the top.

Repeat layering with remaining potatoes and cheese sauce, finishing with the last layer of cheese sauce on top.

Cover the casserole dish with aluminum foil and bake for 30 minutes.

Remove the foil and bake uncovered for an additional 30-45 minutes until fork-tender.

Broil the top for 3-4 minutes for a crispy finish, watching closely to avoid burning.

Let the dish sit for 5-10 minutes before serving to allow the sauce to thicken.