Preheat your oven to 375°F (190°C) for even baking.

Grease a 9×13-inch baking dish with butter or non-stick spray to prevent sticking.

In a medium saucepan, melt 3 tablespoons of butter over medium heat. Whisk in 3 tablespoons of flour to create a roux and cook for 1-2 minutes until golden.

Gradually add 1 1/2 cups of milk, whisking constantly to avoid lumps. Simmer for 5-7 minutes until thickened.

Remove from heat and stir in 1 1/2 cups of grated sharp cheddar cheese until melted and smooth. Season with salt to taste and add a pinch of cayenne pepper if desired.

Layer half of the thinly sliced potatoes in the baking dish, slightly overlapping. Pour half of the cheese sauce over the potatoes and spread evenly.

Repeat with the remaining potatoes and cheese sauce.

Sprinkle 1/2 cup of extra grated cheese over the top of the casserole.

Cover with foil and bake for 45 minutes, then uncover and bake for an additional 15-20 minutes, or until the top is golden and bubbly.

Remove from the oven and allow the dish to rest for 10-15 minutes before serving. Garnish with sliced green onions if desired.